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M.A. (Oxov ), Sc D (TUBINGEN), D Sc. (LEEDS), F R.S. 






London Edinburgh Glasgow Copenhagen 

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Bombay Calcutta Madras Shanghai 


Publisher to the University 


Printed in Great Britain 


HHHIS book aims at giving a general account of the 
-*- principles of valency and molecular constitution, 
founded on the Rutherford-Bohr atom. 

In developing the theory of valency there are two 
courses open to the chemist. He may use symbols with 
no definite physical connotation to express the reactivity 
of the atoms in a molecule, and may leave it to the subse- 
quent progress of science to discover what realities these 
symbols represent : or he may adopt the concepts of 
atomic physics electrons, nuclei, and orbits and try 
to explain the chemical facts in terms of these. But if he 
takes the latter course, as is done in this book, he must 
accept the physical conclusions in full, and must not 
assign to these entities properties which the physicists 
have found them not to possess : he must not use the 
terminology of physics unless he is prepared to recognize 
its laws. I have endeavoured to conform to this prin- 
ciple, and not to lay myself open to the reproach of an 
eminent physicist, that ' when chemists talk about elec- 
trons they use a different language from physicists '. 
I have been careful to avoid as far as possible the 
introduction of any physical hypotheses which are 
not already sanctioned by those who are best qualified 
to judge of them. 

A theory of valency can only be justified by showing 
that it is applicable to chemistry as a whole ; it is not 
enough that isolated examples can be quoted in its 
defence. In the present volume the general principles 
of the theory are discussed, and I propose in a second 

vj. r re] ace 

volume to consider their application to the individual 
elements in detail ; but as this cannot appear for some 
time, I have included here (Chapter XV) a summary of 
the characteristics of the several periodic groups, in the 
light of the results reached in the previous chapters. 
This must involve some repetition in the next volume, 
but it seemed desirable to indicate how these ideas can 
be used to elucidate the relations of the periodic table, 
and of inorganic chemistry generally. 

It has been suggested that the development in the last 
few years of the theory of wave mechanics necessitates 
a fundamental change in our views of atomic structure. 
This theory, in the hands of de Broglie, Heisenberg, 
Schrodinger, and others, has had the most remarkable 
success in dealing with problems of atomic physics, and 
in particular has enabled us to calculate the relative 
intensities of spectral lines, which on the Bohr theory 
was possible only to a very limited extent. These 
results are obtained by treating the electron-in-its- orbit 
as a system of stationary waves, so that the electron as 
a separate entity seems to disappear from physics, and 
it might be thought that we are no longer entitled to 
speak, as we formerly did, of electrons as actual bodies 
rotating round nuclei. But the theory of wave mechanics, 
although there can be no doubt of its value as a calculus, 
has not yet reached the stage at which one can say 
definitely how it is to be translated into physics. It 
gives the right answer to problems hitherto treated as 
questions of probability and statistics, although it may 
be the statistics of a single atom. It has as yet given no 
proof that the physical concepts which led Schrodinger 
to his fundamental differential equation should be taken 
so literally as to be incompatible with the conceptions 

Preface vii 

of the nature of electrons and nuclei to which the work 
of the last thirty years has led. 

Among the books which I have used I have especially 
to acknowledge my debt to Bohr's Theory of Spectra and 
Atomic Constitution, to Andrade's Structure of the Atom 
(of the third edition of which Prof. Andrade was so kind 
as to allow me to read the proofs before publication), to 
Stoner's Magnetism and Atomic Structure, and to G. N. 
Lewis's Valence : and on the chlmical side to Abegg's 
invaluable Handbuch, Werner's Neuere Anschauungen, 
Weinland's Kompleocverbindungen, and Pfeiffer's Orga- 
nische Molekulverbindungen. Other monographs which 
I have consulted are referred to in their place. 

I am also under great obligations to several of my 
friends for assisting me with their knowledge of the large 
range of subjects with which such a book as this neces- 
sarily deals. Prof. F. A. Lindemann has read and criti- 
cized the first three chapters, dealing with the physics of 
the atom, and greatly increased both their accuracy and 
their perspicuity ; Dr. E. C. Stoner has helped me with 
the list of atomic structures and the chapter on mag- 
netism ; Mr. W. H. Mills has given me the benefit of his 
unrivalled knowledge and judgement in the chapters on 
stereochemistry and chelate rings, the latter of which 
has also profited by the criticisms of Mr. T. W. J. Taylor. 
Prof. T. S. Moore has read the whole book in proof, and 
made many useful suggestions. I owe an especial debt 
of gratitude to Mr. M. P. Applebey, who has not only 
read the whole of the manuscript with great care, and 
saved me from many errors and obscurities, but has also 
allowed me to read the manuscript of his lectures on 
inorganic chemistry, which have been of great value to 
me throughout, and particularly in the last chapter. 

vin Jfrcjace 

Mr. L. A. Woodward has helped me with the correction 
of the proofs and the preparation of the index. In grate- 
fully acknowledging the assistance of so many kind 
friends, I feel bound to add that they are not to be held 
responsible for any of the views I have expressed, with 
which they by no means always agree. 

I have further to thank Messrs. Bell and Prof. Andrade 
for permission to use the diagrams on pages 26 and 27. 

N. V. S. 



Chapter I. The Nuclear Atom and Atomic Number . . 1 

Atoms of matter and electricity (1). Thomson's electronic 
theory (2). Scattering of rays by matter (4). Rutherford's 
nuclear atom (5). Positive unit or proton (6). Radioactive 
displacement law (7). Moseley's X-ray measurements (7). 
Atomic number (8). Dimensions of atom and its parts (9). 
Isotopes (11). 

Chapter n. The Bohr Theory : the Hydrogen Atom . -i 14 

Instability of the nuclear atom on classical dynamics (14). 
The Quantum theory (15). Bohr's fundamental postulates 
(18). Application to the hydrogen atom (19). Spectrum 
series of hydrogen (21). Spectrum of ionized helium (22). 

Chapter m. The Bohr Theory : Atomic Structure and the -J 
Periodic Classification . . . .25 

Types of orbit (25). Position of inert gases (28). Charac- 
teristics of the periodic table (29). Subgroups of electrons 
(81). Third quantum number (34). Optical spectra (35). 
Development of the periodic table (38). Types of atoms (45). 
List of atomic structures (48). . 

Chapter IV. Valency : Fundamental Principles . . . ^ 51 

Early views : Berzelius, Arrhenius (51), Werner (52). 
Electronic interpretation : Kossel (54), G. N. Lewis (56). 
Co-ordinate links (59). Valency groups (62). Application to 
simple compounds (64). 

Chapter V. Valency and the Periodic Table . . .74 

Mendeleeff's form of table (74). Expression in terms of 
atomic structure (74). lonization (76). Stable cores (76). 
Distribution of ions in the table (77). Relation of A and B 
subgroups (78). Transition elements (81). 

Chapter VI. Electrovalency and Covalency . . .83 

Criteria (84). Volatility (87). Solubility (89). lonization 
and crystal structure (90). Transition between electro- 
valencies and covalencies : weak electrolytes (92). Orbits 
of shared electrons (98). One-electron covalencies (102). 
Covalency and the periodic table : Fajans' theory (104). 

x Contents 

Chapter VII. Co-ordination .... 109 

Werner's theory (109). Electronic interpretation (112). 
Conditions of co-ordination (116). Donors and acceptors 
(116). Double salts (118). Chelate compounds (119). Pro- 
perties of compounds with co-ordinate links (121). Molecular 
volume : Sugden's Parachor (124). 

Chapter VHI. Molecular Association . . 132 

Normal and abnormal liquids (182). Association and 
co-ordination (184). ' Pure donors ' (137). Solubihtv . 
relation to vapour pressure (188). ' Natural solubility '(111). 
Solubility and structure : examples (145). 

Chapter EX. Covalency Maxima . . 152 

Covalency rule (152). Evidence : for hydrogen (153) : for 
first short period (158) : for heavier elements (155) : covul- 
ency of 8 (156). Confirmatory evidence (156). Actual and 
theoretical maxima (161). 

Chapter X. Stable Valency Groups . . 163 

Determination of Effective Atomic Number (163) : dis- 
tribution into groups (165). Relation of co valency rule to 
Bohr's theory (167). Pure and mixed valency groups (170). 
The octet (173). The atomic core (176). The ' inert pair ' oC 
electrons (179). Absolute valency (182). 

Chapter XI. Solvation . 135 

Definition of molecule in solid phase (185). Hydration of 
salts (189): of cations (192) : of amons (194) : mutual influ- 
ence (196) : excessive hydration (198). Ammonia of crystal- 
lization (200). 

Chapter Xn. Atomic and Molecular Magnetism . . 204 

General principles (204). Langevin's theory (205). Dia- 
magnetism (206). Paramagnetism (207). The Bohr magneton 
(207). Magnetic moments of atomic rays (208). Para- 
magnetic gases (211). Simple paramagnetic ions (211). Com- 
plex ions (214). 

Chapter xm. Stereochemical Relations . .219 

Carbon (219). Nitrogen (220). Beryllium, boron, oxygen 
(221). 6-covalent atoms (223). 4-covalent atoms of 
heavier elements (225). Compounds of trivalent sulphur 
(228). Plane arrangement of 4 co valencies : platinum (229) 
tellurium (281). 

Contents xi 

Chapter XIV. Chelate Rings . . . . .233 

Evidence for their existence (233). Mordant dyes (234) 
Strain theory (286). Types of chelate rings (239). 4-Rings 
(248). 5-Rmgs (245). 6-Rings (247): with two double 
links (248). 7-Rings and 8-Rmgs (251). Co-ordination and 
the carboxyl group (252). 

Chapter XV. The Periodic Groups . . . .256 

Group : Inert gases (257). Group I : Hydrogen (258) : 
Alkali Metals (259) : Copper, Silver, Gold (260). Group II 
(262) : typical elements and subgroup A (263) : Zinc, 
Cadmium, Mercury (263). Group III (264) : Boron, Aluminium 
(265) : subgroup A (266) : subgroup B (267). Group IV 
(268) : typical elements and subgroup B (270) : subgroup A 
(278). Group V : typical elements and subgroup B (276) : 
subgroup A (280). Group VI : typical elements and sub- 
group B (288) : subgroup A (287). Group VII (288) : 
halogens (289) : manganese (294). Group VIII (295). 


Periodic Table (according to Bohr) . . .39 

Periodic Table (after Mendelfeff) . . 75 



25, J. 9, for & ellipse read an ellipse 
30, 1. 7 from bottom, for (Pd 44) read (Pd 46) 
81, 1. 7 from bottom (table), for w 4 read Wj 
48, 1.2, for Pd44 read Pd 46 
107, 1. 13 from bottom, delete except ThCl 4 
120, 1. 6 from bottom (last line of formula), 

for C==CH 3 read 0=C CH 3 

160, 1.4, for 2>0-*S< read IX^K 
189, 1. 15 from bottom, 

for [x<- <gl" read [x-0<|:] + 

227, 1. 15, for thetine i ead aulphonium salt 
276, 1. 5 from bottom, for element read elements 
295, 1. 8 (table), for E 44 read Eu 44 

Contents : 

Chapter XIV. Chelate Rings . . . . .21 

Evidence for their existence (233). Mordant dyes (234). 
Strain theory (236). Types of chelate rings (239). 4-Rings 
(243). 5-Rings (245). 6-Rings (247) : with two double 
links (248). 7-Rings and 8-Rings (251). Co-ordination and 
the carboxyl group (252). 

Chapter XV. The Periodic Groups . . . .2? 

Group : Inert gases (257). Group I : Hydrogen (258) : 
Alkali Metals (259) : Copper, Silver, Gold (260). Group II 
(262) : typical elements and subgroup A (263) : Zinc, 
Cadmium, Mercury (263). Group III (264) : Boron, Aluminium 
(265) : subgroup A (266) : subgroup B (267). Group IV 
(268) : typical elements and subgroup B (270) : subgroup A 
(273). Group V : typical elements and subgroup B (276) : 
subgroup A (280). Group VI : typical elements and sub- 
group B (283) : subgroup A (287). Group VII (288) : 
halogens (289) : manganese (294). Group VIII (295). 


Periodic Table (according to Bohr) . . . .3: 

Periodic Table (alter Mendel&ff) . . . .7. 

List of Atomic Structures .... 48-5< 


Contents xi 

Chapter XIV. Chelate Rings . . . . .233 

Evidence for their existence (233). Mordant dyes (234). 
Strain theory (236). Types of chelate rings (239). 4-Rings 
(243). 5-Rings (245). 6-Rings (247) : with two double 
links (248). 7-Rings and 8-Rings (251). Co-ordination and 
the carboxyl group (252). 

Chapter XV. The Periodic Groups . . . .256 

Group : Inert gases (257). Group I : Hydrogen (258) : 
Alkali Metals (259) : Copper, Silver, Gold (260). Group II 
(262) : typical elements and subgroup A (263) : Zinc, 
Cadmium, Mercury (263). Group III (264) : Boron, Aluminium 
(265) : subgroup A (266) : subgroup B (267). Group IV 
(268) : typical elements and subgroup B (270) : subgroup A 
(273). Group V : typical elements and subgroup B (276) : 
subgroup A (280). Group VI : typical elements and sub- 
group B (283) : subgroup A (287). Group VII (288) : 
halogens (289) : manganese (294). Group VIII (295). 


Periodic Table (according to Bohr) . . . .39 

Periodic Table (after Mendeteeff) . . . .75 

List of Atomic Structures .... 48-50 


Ann. Liebig's Annalen der Chemie. 

Ann. Chim. Annales de Chimie. 

Ann. d. Phys. Annalen der Physik. 

Ber. Berichte der Deutschen Chemischen Gesellschaft. 

Bull. Soc. Bulletin de la Societe chimique de France. 

C. R. Comptes rendus des Seances de 1' Academic des Sciences. 

Chem. and Ind. Chemistry and Industry. 

J. Am. Ch. Soc. Journal of the American Chemical Society. 

J. C. S. Journal of the Chemical Society. ' 

J. de Phys. Journal de Physique. 

J. pr. Chem. Journal fur praktische Chemie. 

Phys. Z. Physikalische Zeitschrift. 

Proc. Nat. Acad. Sci. Proceedings of the National Academy of 

Sciences, Washington. 

Z. anorg. Chem. Zeitschrift fur anorganiscjje Chemie. 
Z. f. Phys. Zeitschrift fur Physik. 
Z. phys. Chem. Zeitschrift fur physikalische Chemie. 

h = Planck's Constant (6-554 x 10~ 27 erg-seconds). 
E.A.N. - Effective Atomic Number (see p. 163). 
Alk -^ Alkyl, C n H 2ntl . 
Ar = Aryl, aromatic radical, as C 6 H 6 . 
Me = Methyl, CH 3 . 
Et = Ethyl, C 2 H 5 . 


IF we disregard mere speculation on the structure of matter, 
our knowledge of the atom begins with the promulgation of 
the atomic theory of matter by Dalton in 1808. This was fol- 
lowed in 1834 by Faraday's enunciation of the laws of electro- 
lysis. For some time the full significance of these laws was not 
appreciated. It was first pointed out by Helriaholtz, 1 who says : 
' Now the most startling result of Faraday's laws is perhaps this. 
If we accept the hypothesis that the elementary substances are 
composed of atoms, we cannot avoid concluding that electricity 
also, positive as well as negative, is divided into definite elementary 
portions, which behave like atoms of electricity^ 2 Faraday's 
laws in fact correspond exactly to Dalton' s laws of constant and 
of multiple proportions : they assert (1) that the amount (and 
sign) of electricity connected with an atomic or other ion is 
constant ; and (2) that if an atom can form more than one kind of 
ion (as cuprous and cupric, or ferrous and ferric), then the amounts 
of electricity combined with the same atom have a simple ratio 
to one another or, as we should now say, the amount of elec- 
tricity combined with a gram-ion of any element is either 96,540 
coulombs or some small integral multiple of that quantity. 

. It was not, however, until the last few years of the nineteenth 
century that any light was obtained on the question of the 
structure of the atom. During these years a series of advances 
of the greatest importance were made, which bore either directly 
or indirectly on the question. In 1894 came the discovery of 
the first of the inert gases by Rayleigh and Ramsay, followed in 
a short time by that of the others. In. 1895 Rontgen discovered 
the X-rays, and this led two years later to the recognition of 

1 Faraday Lecture, J. C. S. 9 1881, 39, 277. 

2 * The Faraday lecture, delivered by Helmholtz before the Fellows of 
the Chemical Society in the theatre of the Royal Institution on Tuesday, 
April 5, 1881, was an epoch-making monument of the progress of Natural 
Philosophy in the nineteenth century, in virtue of the declaration, then 
first made, that electricity consists of atoms. Before that time atomic 
theories of electricity had been noticed and reject edby Faraday and Max- 
well, and probably by many other philosophersandrworkers ; but certainly 
accepted by none. Now in the beginning of the twentieth century we all 
believe that electricity consists of atoms.' Lord Kelvin, preface to the 
English translation of Konigsberger's Life of Helmholtz, Oxford, 1906. 

3 o6a B 

z 'l*he Electron 

radioactivity by Becquerel. About the same time J. J. Thom- 
son, Wiechert, and Kaufmann were engaged in investigating and 
interpreting the phenomena of the electric discharge in high 
vacua (Crookes's ' fourth state of matter '), and arrived in 1897 
at the discovery of the atom of negative electricity the electron. 
If our knowledge of atomic structure is still in many respects 
imperfect, as it is, it must always be remembered that thirty 
years ago we had no certain knowledge that the atom had any 
structure, aiidni^vidence of the existence of anything smaller 
than a whole atflbi. 

The evidence given by Thomson for his electronic theory was 
in outline this, Crookes had shown that when an electric dis- 
charge was passed through a highly exhausted tube, ' rays ' 
were sent out in straight lines from the cathode, which became 
evident when they struck the sides through the green fluor- 
'escence which they produced. Their rectilinear propagation was 
proved by interposing a screen, which cast a shadow in the same 
way as it would have done with rays of light. The nature of these 
rays was disputed, some maintaining that they were charged 
particles, and others that they were forms of vibration in the 
ether. The first view was maintained by Thomson, chiefly 
on the following grounds : (1) that they were deflected by a 
magnetic field in a direction perpendicular to the lines of force, 
as charged particles would be ; (2) that Perrin had shown that 
if the stream of rays were deflected so as to fall on an insulated 
metallic surface, that surface acquired a negative charge ; (8) 
that they were deflected by an electric field. 

The methods by which their velocity, mass, and charge were 
determined are in principle very simple. A narrow beam of the 
rays is exposed to an electric field, and at the same time to a 
magnetic field. The two fields are so adjusted in strength that 
they exactly neutralize one another, and the spot of light pro- 
duced by the rays is not shifted from its original position. Then 
we know that the forces exerted by the two fields are equal. 
Now if e is the charge on each particle, and v its velocity, the 
electric field of strength X will produce a force X e, and a mag- 
netic field of strength H a force H-e-u. Thus at equilibrium 

X-e = H-e-v, or v = . 


As we can measure X and H, we can thus determine v, indepen- 
dent of the value of e. 

The actual velocity of the electrons varies with the conditions 

The Electron 3 

of their liberation, from zero (in the case of a hot wire) to 99-8 
per cent, of the velocity of light, in the case of the fastest /8-rays 
from radioactive substances ; by arranging the conditions, any 
desired velocity within these limits may be obtained. 

The ratio of the electric charge to the mass can be measured 

most easily by abolishing the magnetic field and observing the 

deflection in an electric field alone. If X is again the strength 

_of the electric field, the particle is being deflected exactly as a 

heavy body shot out horizontally is deflected lyjr gravity, and its 


acceleration g is X- . If it moves through a length I with the 

velocity v, the time during which it is exposed to the force is 
l/v, and hence d, the distance through which the spot of light 
moves when the field is put on, is . 

A ^ lXeZ2 

2 2 = ^ = 2^*- 

Hence = -^rr , where d, X, v } and I are all measurable. 
m XZ 4 

Thomson found that if the value of the charge e is assumed to 
be the same as that of the charge of a hydrogen or other uni- 
valent ion, the mass of the electron is 1 /1840 of the mass of 
a hydrogen atom. 1 Subsequently, the actual number was 
counted, by the method of C. T. R. Wilson, of using them as 
centres of condensation of water vapour, and this view of their 
charge and mass confirmed. 

On further investigation it was found that cathode rays could 
be produced by a great variety of methods by electric discharge 
in high vacua, by the action of ultra-violet light on metals, in 
flames, from heated wires, by the action of X-rays, and from 
radioactive substances ; and it was shown by Townsend and 
others that by whatever methods and from whatever materials 
they were produced, though their velocity varied, their other 
properties, and especially the ratio e (m, did not. Thus it is clear 

1 This does not involve a knowledge of the Avogadro number N (the 
number of molecules in a gram-molecule) or of the weight in grams of a 
hydrogen atom. These experiments show that the charge on a gram of 
electrons is 18 million electromagnetic units. That on one gram of hydrogen 
ions is known to be 96,540 coulombs or 9,654 E.M.U. If each hydrogen ion 
has the same charge as one electron (of opposite sign) there must be m one 


gram of electrons or 1860 times as many electrons as there are 

s 9,654 

hydrogen ions in one gram. (These values are only approximate : the exact 
mass of an electron is more nearly 1/1840 of that of a hydrogen atom.) 

4 Scattering of Rays by Atoms 

that the electron, with, a negative charge of 4 77 x 10~ 10 E.S.U., 
and a mass of H /1840, is a constituent of every species of atom. 

A variety of further discoveries of importance gave support 
to this view. In particular, the effect discovered by Zeeman, 
that when a body emitting light is placed in a magnetic field the 
spectrum lines are split up, was shown by H. A. Lorentz to be 
quantitatively explicable on the hypothesis that the emission of 
light is due to electrons of this charge and mass. 

Now the atomSS&re electrically neutral, and so if they contain 
negative electricity in the form of electrons, they must also con- 
tain an equal amount of positive electricity in some form. The 
nature of this was for some time unknown. In his earliest at- 
tempts to deduce a structure for the atom, Thomson assumed 
that the electrons moved in a sphere of uniform positive electri- 
fication. This was avowedly pure speculation, but it enabled 
him to calculate that the successive electrons would arrange 
themselves in concentric rings, and even on certain assumptions 
in rings of eight, suggesting a recurrence of properties at periodic 
intervals in the series of elements, and a relation to the eight 
groups of Mendel^eff s table. 

The discovery of X-rays, and of the rays accompanying radio- 
active change, provided new and powerful instruments for ex- 
amining atomic structure. The difficulty of this problem is the 
difficulty of penetrating into the structure of the atom ; it is 
| only by finding something that can get inside that we can dis- 
' cover what is there. Ordinary matter cannot penetrate into the 
atom, and the atom is so small in comparison with visible light 
that optical methods are of no use : the wave-length of yellow 
sodium light is about 8,000 times the diameter of an atom. But 
the X-rays are much shorter (very hard rays from about one to 
one-tenth atomic diameter), and hence they penetrate the atom 
and are affected by its various parts. The jS-rays of radioactive 
substances are themselves electrons, and have enormous veloci- 
ties, approaching in some cases that of light : while the a-rays 
are very small particles (as compared with the atom) as heavy 
as four hydrogen atoms, and have velocities which may rise to 
a tenth of that of light. These powerful agents can force their 
way inside the atom, and we can infer what is there from the 
effect which it has on them. 

The first experiments carried out by these means were to direct 
a narrow parallel beam of one of these kinds of rays /?-rays from 
a radioactive source on a thin sheet of metal. It is found that 

The Nuclear Atom 5 

the emergent beam is no longer parallel, but is divergent. This 
is the natural result of the repulsion of the ^-particles by the 
electrons in the atoms of the metal. The amount of the diver- 
gence enables us to calculate how many electrons they have met 
in their passage, and therefore how many electrons there are per 
atom. It is found that this depends on the nature of the atom, 
and that the number is about half the atomic weight on the 
ordinary scale, say about 12 for aluminium, an<J about 100 for 
gold. It is thus clear that the freely moving electrons in an atom 
only account for a very small fraction (about 1 /4000) of its mass. 

But in the course of this work a further discovery was made, 
which was of fundamental importance. Geiger and Marsden 1 
exposed a gold leaf to a beam of a-rays. The average scattering 
was 87, in agreement with the general result given above. 
But they found that a small number of particles suffered very 
large deflections, and some were even driven backwards. Thus 
1 in 20,000 were deflected through large angles, the average 
value of which was 90. Now from the mean value of 0-87 it can 
easily be calculated that the chance of a deflection of 90 is 
vanishingly small. Hence it is evident that a new phenomenon 
is taking place. This cannot be a surface reflection, because the 
number of particles so scattered increases in proportion to the 
thickness of the leaf. For the same reason it cannot be due to 
a succession of small deflections, because if it were, the number 
would increase only in proportion to the square root of the thick- 
ness, since we cannot assume that the successive deflections 
would all be in the same direction. 

These facts were pointed out by Rutherford in a paper 2 which 
is the foundation of modern atomic theory and contains the 
statement of the doctrine of the nuclear atom. The a-particle 
weighs more than 7,000 times as much as an electron, and hence 
no collision with an electron (which cannot be moving very much 
faster than the a-particle) could do more than deflect it slightly. 
It can only be turned back by hitting something more or less of 
its own mass, and in order that sufficient force may be developed, 
this heavy particle must have a large electrical charge. Ruther- 
ford points out that ' the theory of J. J. Thomson ' (of the sphere 
of uniform positive electrification) ' does not admit of a very 
large deflection in traversing a single atom, unless it is supposed 
that the diameter of the sphere of positive electrification is 
minute in comparison with the diameter of the sphere of influence 

1 Proc. Roy. Soc. 1909, 82, 495. 2 Phil. Mag. 1911, 21, 669. 

6 The Nuclear Atom 

of the atom '. After considering the dynamics of the problem he 
shows that the determining factor is the charge N0 on this small 
positive nucleus, and that the value of this charge can he calcu- 
lated from the amount of the wide-angle scattering. He finds for 
a series of elements values of N approximately equal to half the 
atomic weight, that is, equal to the number of free electrons in 
these atoms as deduced by Crowther from the scattering of 
0-rays, and subsequently by Barkla from that of X-rays. There 
can thus only be one of these nuclei in the atom, since its charge 
is equal to that of all the free electrons. 1 

Rutherford's theory therefore is that the atom consists of a 
small nucleus containing the whole positive electricity of the 
atom, and practically the whole of its mass ; this has a charge 
of Nxe units of positive electricity, and is surrounded by 
N negative electrons, which form with it a neutral atom. 

On this theory all subsequent developments of the theory of 
the atom have been built. The idea of a nuclear atom had been 
suggested earlier by several physicists, but without any evidence 
in its support. The evidence adduced by Rutherford is so simple 
and direct, that no serious effort has been made to dispute it. 

It still remains to discover what the atom or unit of positive 
electricity is. Now the hydrogen atom contains the lightest 
nucleus known, and has one attendant electron. Its nucleus 
therefore has a charge equal to that of an electron. In a suitable 
discharge tube we can get positive rays consisting simply of the 
hydrogen atoms which have lost their attendant electrons. These 
are the lightest positively charged atoms which we can obtain. 
It is also noticeable that while most elements will give positive 
rays consisting partly of doubly and trebly charged atoms, the 
"'hydrogen atom can never acquire more than one positive charge. 
For these and other less direct reasons it is practically certain 
that the hydrogen nucleus is the actual unit of positive electricity 
corresponding to the electron, having the same charge but of 
opposite sign, and a mass of 1-007 (0 = 16). This is known as the 

, In his paper Rutherford drew attention to the great impor- 
tance of the magnitude of the nuclear charge Ne as determining 
the properties of the atom. The importance of the number N 
became further emphasized as the result of two different lines of 

1 A further proof is that if there were several nuclei in the atom, the 
ratio of the specific heats of gases at constant pressure and constant volume 
could not be as high as 1-67 even for monatomic gases. 

Charge on the Nucleus 7 

research. The study, of radioactive changes showed that when 
an atom disintegrates, it gives off either an a-particle a helium 
nucleus with a double positive charge or a /?-particle, an 
electron ; and the energy of these particles proves that they 
come from the nucleus. Early in 1918 it was pointed out simul- 
taneously by Russell, 1 Fajans, 2 and Soddy, 3 that when an 
element undergoes an a-ray change it moves two places in the 
periodic table to the left (i.e. towards hydrogen) ; for example, 
radium in Group II becomes emanation in Group O : and when 
it undergoes a -ray change, it moves one place to the right 
(towards uranium). This is what one would expect if every 
successive element had a nuclear charge one unit larger than 
that of its predecessor, the a-particle carrying off two positive 
charges and so reducing the charge on the nucleus by 2, whilst 
the /f-particle removes one negative unit, and so increases the 
nuclear charge by 1. 

. The hypothesis that successive elements differed by one unit in 
their nuclear charge that every possible nuclear charge from 
1 to the highest known was represented by a different element 
had been suggested quite definitely by van den Broek in 1911 ; 4 
but as it was not supported by any very definite evidence, and 
indeed in its original form was related to an incorrect form of the 
periodic table, it did not attract much attention., 

The radioactive evidence was confined in the first instance to 
the radioactive elements, and its applicability to the lighter 
elements was uncertain. The whole question took on a different 
aspect in the light of the work of Moseley in the same year. 5 He 
measured the wave-length of the X-rays given off by various 
elements when bombarded with cathode rays, by means of a 
potassium ferrocyanide crystal used as a grating. The full 
significance of his work can only be understood in relation to the 
Bohr theory of atomic structure ; but even without regard to 
this or any other theory, his results are sufficiently remarkable. 
He showed that the frequencies of the radiations were charac- 
teristic of each element : that if the square root of the frequency 
of the hardest ray (i.e. with highest frequency) was plotted 
against a value for each element called the atomic number, it 

i A. S. Russell, Chem. News, 1913, 107, 49 (Jan. 81). 

a K. Fajans, Phys. Zeitschr. 1913, 14, 131 (Feb. 15). 

8 F. Soddy, Chem. News, 1913, 107, 97 (Feb. 28). 

4 Nature, 1011, 87, 78 ; 1913, 92, 872 ; Phys. Zeitschr. 1913, 14, 32. 

8 Phil. Mag. 1913, 26, 1024 ; 1914, 27, 708. 

o Atomic Number 

gave a straight line : and that the atomic number required to 
give this relation is the ordinal number of the element in the 
series of elements arranged according to their atomic weights. 
This relation held for all the elements he examined from alu- 
minium (taken as 18, since it was the thirteenth of the known 
elements), to gold 79, except in three cases (A, K : Co, Ni : Te, I) 
where the order of atomic weights was already known to disagree 
with the order of chemical properties, and with the further 
proviso thaj four of these elements (43, 61, 72, 75) still remained 
to be discovered. 1 This conclusion is sufficient to show that, 
as he says : ' there is in the atom a fundamental quantity which 
increases by regular steps as we pass from one atom to the next. 
This quantity can only be the charge' on the central positive 
nucleus.' If we apply the Bohr theory, we can show that the 
wave-lengths which he obtained agree quantitatively with those 
required by the theory, on the assumption that the known 
elements correspond to all possible integral values of the nuclear * 
charge (with the exception of six, of which four have since been 
discovered) from 1 to 92. 

We may summarize the conclusions so far arrived at as follows. 
All atoms are composed of positive units of electricity or protons 
and negative units or electrons : each of these has a charge of 
4-77 x 10~ 10 electrostatic units. The" mass of the proton is 
1-007 (taking the weight of the oxygen atom as 16) and that of 
the electron is 1/1840 or 0-00054. The protons are all collected 
in a very small volume forming the nucleus, and are surrounded 
by a number of electrons sufficient to neutralize their charge. 
Thus the atomic number is at once the ordinal number of the 
element, the positive charge on the nucleus, and the number of 
electrons surrounding the nucleus. Now since practically the 
whole mass of the atom is due to the protons, and each of these 
weighs as much as a hydrogen atom, every atom must contain 
in the nucleus a number of protons equal to its atomic weight 
on the ordinary scale. The atomic number is abqut half this. 
Hence the number of protons in the nucleus must be about twice 
the nuclear charge. This means that the nucleus must contain 
electrons as well as protons and about half as many electrons 
as protons to neutralize part of its charge. For example, 
sodium, atomic weight 23, atomic number 11, must have 28 
protons in the nucleus to give it its mass, and, therefore, 12 

1 There were (and still are) also two other elements missing beyond 
gold, 85 and 87 : in these the nucleus is probably too unstable to exist. 

Dimensions of the Atom 9 

electrons also in the nucleus to neutralize 12 of them and leave 
a balance of 11 positive units. This nucleus (28 + , 12 ) is 
surrounded by 11 electrons, forming a neutral atom. In the 
same way iodine (atomic weight 127, atomic number 53) must 
have in the nucleus 127 protons and 127 58=74 electrons; 
and this nucleus is surrounded in the neutral atom by 53 electrons. 
In general, an atom of atomic weight A and atomic number Z 
will have a nucleus of A protons and A Z electrons, surrounded 
by Z other electrons. 

At this point we may consider briefly the magnitude of the 
atom and its parts. It would take us too far to discuss the evi- 
dence for this ; but it should be said that we make the assump- 
tion, which is now generally accepted, that the mass of the 
proton and of the electron is solely due to their electrical charge. 

The number of atoms in a gram-atom for example, of hydro- 
gen atoms in 1 gram, or of sodium atoms in 23 grams (the 
Avogadro number) is 6 06 x 10 23 . This figure does not convey 
much as it stands, but some idea of its meaning may be got from 
two facts. If a tumblerful of water is poured into the sea, and 
in the course of time this becomes uniformly distributed through 
the sea, the rivers, and all the other waters in and surrounding 
the earth : and if then a tumblerful of water is taken from any 
sea or river, this will contain about 1,000 of the molecules that 
were in the original tumbler. Another illustration has been 
given by Aston. Take an ordinary exhausted electric light bulb, 
and let a minute hole be made in the side, just big enough to let 
through a million molecules every second. 1 It will be 100 million 
years before the bulb is filled with air at atmospheric pressure. 

To get an idea of the dimensions of the atom and its parts we 
must multiply them by some factor which will make them of a 
more familiar size. We may take the factor suggested by Dar- 
win, 10 13 : JJ) 13 cms. is about two-thirds of the way to the sun. 

The dimensions are : * ., 7 -I/MS 

Actual. x 10 13 . 

Diameter of atom . 2 - 4 x 10~ 8 2-4 kms. 
electron . 1 88 x 10~ 13 1 88 cms. 
proton . 1 x 10~ 18 1/100 mm. barely 

nucleus (not 
hydrogen) 3 80 x I0~ 13 say 1 inch to 1 foot. 

1 The hole must be supposed to be gradually enlarged so as to keep this 
rate constant as the pressure inside the bulb increases. -^ 
3062 C 

10 The Nuclear Atom 

So if we had one of these magnified atoms with its nucleus before 

us, the protons would be scarcely visible : the electrons would be 
about as big as sixpences or acorns (whatever their shape may 
be) and the nucleus, according to whether it was a light or a 
heavy atom, might be anything from the size of a cherry to that 
of a football. Round this nucleus the electrons would be re- 
volving, the nearest pair (which produce the X-rays) a few feet 
off, and the farthest, which are the valency electrons, those that 
take part in chemical combination, moving in orbits which at their 
greatest distance are from half a mile to a mile away. The other 
planetary electrons would be distributed between these limits. 

Perhaps the most surprising conclusion from these discoveries 
is the enormous proportion of the atom which is empty space. 
The density of the proton is about 10 24 and that of the electron 
about 10 11 times that of water. All the protons and electrons in 
the body of an average man if they could be brought close 
together would occupy less than a millionth of a cubic millimetre. 

In considering the properties of the atom, and the parts played 
by different portions of its structure, we have to distinguish 
sharply between the nucleus and the electrons round it. The 
essence of the atom its true individuality resides in the 
nucleus. It is only under exceptional conditions that the nucleus 
can be altered, and when this does happen, a new element is 
formed. This is the real transmutation of matter. On the other 
hand, the surrounding or planetary electrons or at any rate 
some of them are quite easily removed and as easily replaced. 
Whenever an atom is ionized, whether by chemical combination, 
or by exposure under suitable conditions to the action of light, 
heat, or electricity, it gains or loses one or more electrons. For 
example, if a gas such as helium is ionized by heat or X-rays, the 
atoms split off one or more electrons leaving positively charged 
ions. When the exciting force is removed, the ion picks up a 
wandering electron, and returns to its previous neutral con- 
dition. But if the nucleus loses an electron, as happens in a 
-ray radioactive change, the atomic number goes up by one : 
a new element has been formed, and the nucleus can never, so 
far as we know, regain the electron which it has lost. The loss 
of this electron (the -ray ) gives the atom a positive charge ; and 
this is soon neutralized by its taking up another electron : but 
the new electron does not go into the nucleus ; it takes its place 
among the planetary electrons, giving a neutral atom of atomic 
number one more than we started with. . 

Isotopes 11 

The charge on the nucleus the atomic number determines 
the number of electrons which surround it, and also to a very 
high degree of approximation the shapes of their orbits : the 
mass of the nucleus has only a minute effect (see p. 2"3), since it is 
in any case large in comparison with that of the electrons, and 
the gravitational forces are negligible in comparison with the 
electrical. The chemical and (so far as they do not depend 
directly on the mass) the physical properties are determined by 
the number and shape of the electronic orbits, especially of those 
farthest from the nucleus, for when two atoms approach one 
another these external orbits are first affected, and their defor- 
mation shields the inner electrons, and still more the nucleus, 
from the influence of the other atom. Hence every atomic 
number corresponds to a definite set of chemical and physical^ 
properties, that is, in ordinary language, to a definite element. 
If an equal number of protons and electrons were added to the 
nucleus, its mass would be increased while its nuclear charge 
remained unaltered. This would lead to the production of what 
Soddy has called an isotope an element of the same atomic 

f number but a different atomic weight. Two isotopes will thus 

have the same number of planetary electrons, moving under the 

: electrostatic attraction of the same nuclear charge. The differ- 

ence in the mass of the nucleus must have some effect on the 

[ shape of the orbits and therefore on the chemical and physical 

j* properties of the atom ; but this effect is so small that it can only 

be detected with difficulty even in those properties which can be 
measured with the highest accuracy. The one element of which 
the isotopes can be obtained in any quantity in a state of approxi- 
mate purity, so as to render this test possible, is lead. Lead is 
the final product of the radioactive change both of uranium and 
radium, and of thorium. The isotope formed from uranium 
should have an atomic weight of 206, and that froiji thorium 
of 208, as is shown by the following summary of the radioactive 
transformations (with the consequent changes of atomic number 
and weight) which these elements undergo : 

At. No. 92-16+6 82 

U - 8a - 6 = Pb : nucleus 206 + , 124 -. 
At. Wt. 238 - 32 206 

At. No. 90-12+4 82 

Th - 6a - 4 = Pb : nucleus 208 + , 126 -. 
At. Wt. 232 - 24 208 

12 The Nuclear Atom 

The atomic weight of ordinary lead is 207 2. Richards hi 
obtained lead from cleveite of at. wt. 206-08, and Honigschmi 
has got lead from thorite of at. wt. 207- 9. 1 Richards has coir 
pared the properties of light uranio-lead with those of ordinar 
lead . He finds the melting points of the metals and the refractiv 
indices of the salts to be identical. The density of the metal an 
the solubility of its salts as expressed in weight per cent, ar 
exactly proportional to the atomic weights, from which it follow 
that the atomic volume and the molecular solubility of the salt 
are identical. The spectrum has been found by Aronberg 2 an< 
by Merton 3 to show a definite but very small difference, ap 
proaching a hundredth of an Angstrom unit. For all practice 
purposes therefore the isotopes may be regarded as identical ii 
all properties not directly dependent on mass. 

The theories of the nuclear atom and of atomic number are th< 
foundation of modern atomic theory. The first established th< 
dual nature of the atom ; it is composed of a minute centra 
nucleus containing both protons and electrons, but an excess o 
the former : and this nucleus is surrounded by a cloud of elec 
trons sufficient in number to restore the electrical neutrality 
The concept of atomic number gives us as it were the empirica 
formula of the atom : it tells us what the charge on the nucleus 
is, and by how many electrons it is surrounded. There remains 
the question of the constitutional formula of the arrangement oJ 
these electrical units ; and this again falls into two parts, the struc- 
ture of the nucleus, and the structure of the surrounding electrons. 

Of the structure of the nucleus comparatively little is yet 
known. Remarkable progress is being made in several directions, 
but the problem of investigating ' the inside of the inside of the 
atom ' as Rutherford puts it, is still in a very early stage. More- 
over the problem is one which has only an indirect bearing on 
chemical questions, so that, in spite of its great intrinsic interest, 
it will not be further discussed here. 

With regard to the arrangement of the electrons surrounding 
the nucleus, our knowledge is much greater ; and it is this part 
of the atom which determines the chemical behaviour. The only 
theory as to their distribution which can claim any physical basis 

1 Richards and Wadsworth, J. Am. Ch. Soc. 1916, 38, 2613 ; Honig- 
schmid : see Fajans, Z. Elektrochem. 1918, 24, 168 ; also Homgschmid, 
ibid., 1919, 25, 01. 

2 Proc. Nat. Acad. Sci. 1917, 3, 710 ; Astrophys. Journ. 1018, 47, 96. 
2 Proc. Roy. Soc. 1919, 96 A, 388 ; 1921, 100 A, 84. 

The Nuclear Atom 


is that of Bohr, which will be described in outline in the next 
chapter. This theory has had such a wonderful success in ex- 
plaining the spectra both optical and X-ray of the elements, 
that its fundamental truth cannot be doubted, though we may, 
of course, expect that with further investigation it will undergo 
modifications in detail ; and its application to the chemistry of 
the elements is the main subject of this book. 



years after Rutherford had brought forward his sug 
gestion of the nuclear atom, Bohr produced his first paper a\ 
the subject. 1 He pointed out that such an atom was unstabl 
on the ordinary principles of electrodynamics. In J. J. Thorn 
son's model the electrons were assumed to be at rest under tb 
combined influence of their mutual repulsions and the attractioi 
to the centre caused by the uniformly distributed positive electri 
fication, this latter force being proportional to the distance of the 
electrons from the centre. They would thus take up a stablf 
group of positions, that is, one which would persist, and to whict 
they would revert if they were disturbed from it. But in the 
Rutherford atom, in which all the positive electricity was col- 
lected at the centre, the electrons could not be at rest, or they 
would obviously fall into the nucleus. Rutherford supposed 
that they were rotating round the nucleus, whose attractive 
force was balanced by the centrifugal force acting on them, much 
as the planets are retained in their orbits against the sun's 
attraction ; but he did not discuss the nature of the orbits in 
detail. Bohr pointed out that on the classical theory of electro- 
dynamics such an arrangement could not be permanent. An 
electron moving in an orbit is a charged body subject to a con- 
tinuous acceleration towards the centre of the orbit, and when 
a charged body is accelerated it must, on the Maxwell theory, 
radiate energy. Hence the electron should be constantly radi- 
ating energy and approaching the nucleus, and this process 
would only stop when it was actually in contact with the nucleus : 
that is, when the atom, having radiated an enormous amount of 
energy, had contracted to about a ten-thousandth of its original 
diameter. | 

Now some years before Bohr's paper was published, physicists 
had been compelled to recognize that the laws of ordinary dyna- 
mics could not be applied without modification to the processes 
of radiation. We must briefly consider the evidence which led 
to this conclusion, and the modification of these fundamental 
laws which it had been found to necessitate. 2 

1 Phil. Mag. 1918, 26, 476. 

2 See Jeans, Report on the Quantum Theory, Physical Society, London, 
1st ed. 1914, 2nd ed. 1924. 

The Quantum Theory 15 

' Classical ' dynamics the dynamics on which we were all 
brought up is founded on Newton's laws. It assumes that 
these principles, which can be verified (within the limits of ex- 
perimental error) for the motions of the stars, and of masses of 
matter which we can handle, can be applied equally well down 
to the smallest quantities that exist. On this theory the motions 
and interactions of bodies are assumed to be continuous, and 
a body passing from one state to another is conceived to pass 
through an infinite series of intermediate states. Now it has been 
shown, primarily by Planck, Poincare*, and Jeans, that if these 
principles are applied to certain mechanical systems, they lead 
to results diametrically opposed to the facts. For example, sup- 
pose we have a volume of air enclosed by walls impermeable to 
energy, and containing a system of heavy particles, say shot, 
supported by springs. If the shot are set vibrating, and then the 
* system is left to itself, we know that they will gradually com- 

municate practically all their kinetic energy to the particles of 
air, whose velocity will thus be somewhat increased. This is 
generally expressed by saying that the friction of the air brings 
the shot to rest, and the air is thus slightly warmed. A dynamic 
investigation shows that according to Maxwell's theory of equi- 
partition of energy the energy is ultimately so divided that each 
shot has as much as each air molecule : so that if there are 
twenty shot in a litre of air (3 x 10 22 molecules), the shot will 
only retain ICT 21 of their original energy. So far, theory and 
observation seem to agree. But in a vessel containing a gas there 
7**' is besides the molecules of the gas something which we may call 
ether or we may call space, but anyhow something which is 
certainly capable of taking up energy in the form of radiation ; 
and this ether, if it is not continuous, must consist of particles 
far smaller than the atom. Here again by the equipartition 
principle the energy will distribute itself s t o that each ether 
particle has as much as a gas molecule ; and as the ether particles 
are far more numerous, nearly all the energy (all of it if the 
medium is continuous) ought to pass from the matter to the 
ether. But we know how energy is divided between matter and 
ether, and that in fact the matter has many million times as 
much as the ether (for example a mass of iron in a vacuum at 
contains 8xl0 9 ergs, per c.c., and the ether only 4xl(T 21 ). 
So there is clearly something wrong with our principles. But 
there is a further difficulty with respect to the ether itself. Just 
as most of the energy goes from the larger particles to the smaller, 

16 The Quantum Theory 

so the energy of vibration in the ether will tend to pass from t 
longer to the shorter waves : and in radiation at equilibrium 
can be shown that even on the most favourable assumpti' 
all except less than a millionth of the energy of the spectru 
would be in waves shorter than the extreme ultra-violet. B 
the actual distribution is quite different : the maximum ener, 
is at ordinary temperatures in the extreme infra-red, ai 
even in sunlight (6000) it is only in the yellow of the visit 

Many other examples might be given in which the deductio 
from classical dynamics are not in accordance with the observ 
facts. The light emitted by an incandescent gas is in some w; 
connected with the motions of parts of the atoms, and sin 
these, on the ordinary theory, can have an infinite number 
orbits, the spectrum should be continuous : but in fact 
is discontinuous. Again, the atomic heats of the elemen 
should all have a value of about 6 from the absolute zero i 
to the ordinary temperature and above : but in fact they fi 
off rapidly at lower temperatures, approaching and sometim 
reaching (so far as can be observed) in the neighbourhood 
the absolute zero. 

j It is -fijnlp clear that the old continuous dynamics, though it 
quite satisfactory when we are dealing with large masses, brea 
down when we apply it to atoms and their radiations. To me 
this difficulty Planck in 1900 put forward his theory of quanl 
He assumes that energy of vibration cannot be given out 
taken up continuously, but only in definite portions, which 
calls quanta of energy. These quanta are not atoms, in t 
sense in which we call matter and electricity atomic : their size 
fixed, but depends on the frequency of the emitting or a 
sorbing body, or of the radiation, being equal to this frequen 
v multiplied by a universal constant h, which has the val 
6 554 x 10"" 27 erg-seconds. Thus for the D line of sodiu 
(5890 A.U., or 5-89 x 10~ 5 cms.) : 

" 50flxl " 

and the quantum, the product of this by h, is 8-8 x 10' 12 erg; 
this seems a small quantity, but it means that if 28 grams 
sodium give out this quantum, they emit 50 kg. calories. 

It must be observed that translational energy is not subjei 
to quantum limitations : for a particle moving in a straight lir 

Quantum Theory and Atomic Structure 17 

y=0, and so hv=0 : the interchange in this case is so far as 
we know continuous. 

This is the fundamental idea of the quantum theoryjthe truth 
of which is no longer in any serious doubt. Its justification, 
which cannot be further discussed here, lies in the enormous 
number of facts in molecular and atomic physics which it ex- 
plains, and in the quantitative agreement in the values of the 
Planck constant h deduced from quite different classes of 
phenomena. 1 The mechanism of the quantum emission the 
cause of this limitation of the transference of energy is one of 
the outstanding unsolved problems of modern physics. But 
we are concerned now not with the cause, but with the fact ^ 

(The problem of atomic structure is precisely of the kind to 
which we should expect the quantum theory to apply. It was in 
connexion with the general question of radiation that the break- 
down of continuous dynamics was detected, and it was to over- 
come this difficulty that the quantum theory was invented. } We 
should expect a similar difficulty to arise in explaining the electro- 
magnetic radiation of the electrons, and a similar solution 
through the application of the quantum theory to be applicable 
to this case also. This application was the subject of Bohr's 
paper of 1918. 

(As we have seen, he began by pointing out that the Rutherford 
nuclear atom is unstable on the classical theory of Maxwell : the 
electrons as they rotate in their orbits should on that theory be 
continuously radiating energy, and should, therefore, get nearer 
and nearer to the nucleus until finally they fall into it. As the 
dimensions of the atom prove that the electrons have not done 
this, the only alternatives are to suppose either that the electrons i. 
can under some conditions rotate without emitting energy, or// 
they do not rotate at all. 

If the electron is at rest, we have to call in some wholly un- 

1 ' The idea of quanta was first introduced by Planck nearly twenty -five 
years ago in order to account for the distribution of energy in the spectrum 
of complete radiation . Its triumphs in predicting or explaining successively 
the velocity of electrons emitted by metals under the influence of light, the 
atomic heats of solids at low temperatures, the chemical constants of the 
simpler substances, the spectral series of the lighter elements, the X-ray 
spectra of all the elements and the various atomic constants have assured 
it a permanent place in physical thought, and there can be little doubt that 
it forms the outstanding discovery of our generation.' (Lindemann, 
Aristotelian Society, 1924.) 

3061 D 

18 Bohr's Fundamental Postulates 

known force to prevent it from falling into the nucleus, as in 
the static models of J. J. Thomson and Langmuir ; and as we 
have no means of knowing the laws of action of this force, we 
cannot hope to draw any useful deductions from it. 1 It there- 
fore seems better to try what can be done on the lines of the 
quantum theory by assuming that the electrons do rotate, but 
that they do so without radiation of energy, and hence without 
contraction of the orbits. We are then dealing with a system 
subject to the action only of known forces : the Coulomb force 
between electrical charges, and the centrifugal force due to the 
inertia of the electrons. 

Bohr's theory is based on two fundamental postulates^ 
1. He assumes that among the infinite number of orbits pos- 
sible according to continuous dynamics, there is a series in each of 
which the electron can continue to revolve without radiation of 
energy : these he calls the stationary states, meaning not that 
the electron is stationary, but that the orbit is so. In any one 
of these states the electron is subject only to electrical and 
inertia,] forces, and so its orbit can be calculated in much the 
same way as 'that of a planet. These states are distinguished 
by the fact that in them the electron possesses an integral number 
1, 2, 3, &c. of quanta of energy, denned by the equation 
E = nhv, where v is the frequency of rotation, h Planck's uni- 
versal constant and n an integer. 2 This quantizing of the energy 
of the rotating electron, a very different system from the oscillator 
on whichPlanck had based his theory (of which the frequency was 
constant independent of the energy, and equal to that of the 
emitted radiation), was a bold assumption, guess, or inspiration 
which was justified by the agreement of its results with the 
observed facts. 

2. The second assumption is that the electron radiates energy 

(in the form of light or otherwise) only when it passes in a 

quantum jump ' from one of these stationary states to another 

* The arguments in favour of the dynamic as opposed to the static model 
^summarized by Millikan m his Faraday Lecture, J. C. 8. 19^ 125, 

it' S S T- 1 ? e y u ressed b y yfo* that the angular momentum is an 
integral multiple of h/2r : thus for a circular orbit 



mvr = n 


' Bohr's Theory of the Hydrogen Atom 19 

of smaller energy. If its energy in the first state is E 19 and 
in the second E 2 , it must give out the difference Ej E 2 , 
and the frequency of the emitted radiation 1 is assumed to be 
given by 

hv = Ej Eg, or v = 1 * . 

This second postulate involves a departure from the original 
quantum theory, in that Planck obtained his radiation formula 
for an oscillator the frequency of which was constant and inde- 
pendent of its energy, and equal to the frequency of the emitted 
light, while no such simple relation can hold for the atom. As the 
energy of the orbit increases, the frequency of rotation changes 
(with hydrogen it is inversely proportional to the cube of the 
quantum number) ; hence it is not the same in the orbit which 
the electron leaves as in that to which it goes, and neither of 
these values is in general identical with that of the emitted 
light. Einstein has, however, shown 2 that this extension of 
Planck's theory is legitimate, and satisfies the observed laws of 

The application of these ideas to the hydrogen atom, in which 
there is only a single electron, is comparatively simple, and 
affords the strongest evidence of the truth of Bohr's theory. If 
we suppose an electron to approach the nucleus from infinity, it 
will begin rotating in a very large orbit (n=cc), and will then 
jump successively to smaller orbits, emitting light each time as 
its energy diminishes, until finally it reaches the smallest orbit 
(n=l). In any one orbit the attraction of the nucleus must 
balance the -centrifugal force, and therefore we can calculate 
the orbit and find W, the work required to remove the electron 
* from that orbit to infinity : this is - E, and increases as the 

electron approaches the nucleus : the difference between its 
values for any two orbits is the amount of energy (E t E 2 = hv) 
which is evolved as radiation when the electron jumps from one 
of these orbits to the other. 

The relative values of these constants for the successive 
(circular) orbits in a hydrogen atom can thus be calculated, and 
are very simple. 

1 It will be observed that on this theory, while the electron can lose 
several quanta in one ' jump ', these appear only as a single quantum of 
emitted radiation. 

2 Phys. Z. 1917, 18, 121 ; quoted by Andrade, Structure of the Atom, 
2nd ed. 1926, p. 853. 


20 Bohr's Theory of the Hydrogen Atom 


i Quantum Frequency Work E of Velocity 

,\ \ Number. Radius. of Revoln. Removal. in Orbit. 

l!j' 11111 

'I 1 2 4 

'i ft ft 

,'' 4 16 & & i 

,! n n* n 8 w a n- 1 

|i Bohr's second postulate was of enormous importance in that 

ij for the first time it gave a meaning to the complicated relations 

'i of line spectra. The accuracy of spectroscopic measurements 

i (of the order of one in a million) had made it possible to discover 

'[ ' very detailed relations among the various lines of a spectrum : 

I , but they did not in any way resemble those to be expected on 

I the prevalent theory. It was supposed that the frequency of the 
j , emitted light was identical with that of some moving part of the 
lj . atom, in which case one would expect to find some kind oi 

I 1 harmonic relation between the frequencies of different lines. 
;; No such relation could be detected : but on the other hand it 
|i was found that the observed frequencies could be obtained by 
'i taking all possible differences between the members of a series 
'j of ' spectral terms ' characteristic of the element in question 
I (Ritz's combination principle). No explanation of this remark- 
able result could be given until Bohr's second postulate made it 

| clear that these terms were the energies of the stationary states 

j divided by the Planck constant (v = Ej^/h E 2 /A). 
! Thus^for atomic hydrogen the work required to remove the 

( electron from the nfh orbit to infinity is proportional to 1 /n 2 : 

" = W2 

where R is a constant which will be discussed later. Hence, 
when the electron jumps from the nth to the njth orbit the 
energy radiated 

E,-, RA RA , 

n %. = j * = hv 

1 n 2 n^ 


v = 

Now in the spectrum of hydrogen there are a series of pro- 
minent lines known as Ha, H/J, Hy, &c., whose frequencies were 

Spectrum Series of Hydrogen 21 

shown by Balmer in 1885 to be accurately expressed by the 

formula v = R ( --) , where n = 3, 4, 5, &c. To 
\2* n ' 

give an idea of what is meant by accuracy in spectroscopic work, 
the observed and calculated values of some of these lines are 
quoted (the last line was not discovered until later). 


v calculated. v observed. 

Ha n - 8 456 995 X 10 B 456 996 X 10" 

H/3 n - 4 616 943 616 948 

Hy n - 5 690 976 690 976 

HS n - 6 781 192 731 193 

He n - 7 755440 755441 

'Hv' n =20 814865 814361 

By the time of Bohr's paper two other series of hydrogen lines 
were known, the Lyman series in the ultra-violet and the Paschen 
series in the infra-red, to which a third, the Brackett series, has 
since been added : these are given with equal accuracy by the 

Lyman : v = R (-- ,) : n = 2, 3, 4, &c. 

VI 2 n 2 / 

Paschen : v = R ( -\ : n = 4, 5, 6, &c. 

\3* n z / 

Brackett : v = R ( ) : n = 5, 6 ; 
4 n ' 

all with the same value of R. The explanation evidently is that 
in the Lyman series the electron jumps to the first, in the Balmer 
series^o the second, in the Paschen series to the third, and in the 
Brackett series to the fourth quantum orbit. 

A further confirmation of the truth of the theory is that if we 
calculate the diameter of the first orbit to which the electron 
returns, and which in the ordinary unexcited state of the atom 
it occupies, we find it to be 1 08 x 10~ 8 cms., which is of the 
same order of magnitude as that deduced from quite different 
phenomena, such as the viscosity of the gas. 

Again, Bohr showed that on his theory the constant R can be 
expressed in terms of other known constants thus : 

22 Bohr's Theory of the Hydrogen Atom 

where m, e are the mass and charge of the electron, 'Ne is i\ 
charge on the nucleus (N thus being 1 for hydrogen), and c is t? 
velocity of light. The value of R from the spectroscopic dat 
is 1-09675 x 10 s . The value calculated for the right hand sid 
of the equation from the most accurate data known when Bot 
wrote is 1-09 x 10 5 (the most recent values give 1 096 x 10 5 ). 
A further confirmation of great value arose as follows. In 189 
Pickering had observed in the spectrum of the star ^ Puppis 

series of lines of the general formula v = R ( - - J 

R having the same value as in the Balmer series. Rydber 
naturally assumed from the close resemblance of this to th 
Balmer series that these lines also were due to hydrogen, and h 

predicted a series v = 'R,( < -r^ -- 3), one of which was ac 

tually discovered in a stellar spectrum. Fowler afterwards fount 

a series v = R (/-r^ / - TTa) m tne spectrum given b; 

(z) ( n + t) 
a mixture of hydrogen and helium. No place could be found fo 

any of these series in the hydrogen spectrum on Bohr's theory 
Bohr, however, pointed out that there was no evidence tha 
these lines were due to hydrogen : they occurred either in th 
spectra of stars, or in that of a mixture of hydrogen and helium 
They might, therefore, equally well be due to helium, and ii 
singly ionized helium He + we have a system of a nucleus anc 
a single electron, resembling the hydrogen atom in every waj 
except that the nucleus has a double charge (and the diameter o 
the orbit is only half that of the hydrogen orbit of the same n) 
Hence, in Bohr's formula for R, N is now 2, and the constanl 
should be four times as large as for hydrogen. Thus the Picker 
ing equation should be written 

" = 4R (4~x~22 ~ 4 x (n + i)*/ 

(2n + 

(Lines corresponding to even values of the second term were not 
then known, since they lie so close to the Balmer lines : they 
have however since been observed.) So also in the other series, 
since all the denominators have to be quadrupled the half quanta 
disappear, and the lines are seen to be those required by the Bohr 
theory for singly ionized helium. 

Spectrum of Ionized Helium 23 

Shortly afterwards Fowler showed that the Pickering lines can 
be produced in a tube containing pure helium, and therefore 
must be helium lines. 

No sooner had this difficulty been triumphantly overcome 
than another appeared. Fowler showed that the ratio of the 
constant for these ionized helium lines to that for hydrogen is 
not exactly 4 but is 4-0016. This is beyond the range of spectro- 
scopic error. (Bohr replied by pointing out that in the original 
deduction of R it had been assumed that the nucleus was at the 
centre of the electronic orbit, whereas of course the real centre 
is the centre of gravity of the system nucleus 4- electron : in 
other words the mass of the electron had been neglected in com- 
parison with that of the nucleus. Since the latter is 1840 times 
as heavy as the former, the error is small : but for exact accuracy 


the Bohr value of R should be multiplied by.r= , where M' 

* J M + m 

is the mass of the nucleus, and m that of the electron. As this 
correction is larger for hydrogen (M/m = 1840) than for 
helium (M/m = 7860) the ratio of the constants will not be 
exactly 4 : 1 but will be 4 00163 : \.v } 

Yet a further verification of the theory for these two spectra 
was given by Sommerfeld. We have so far assumed the orbits 
to be circular, and on the simple Bohr theory the energy is the 
same whether they are circular or elliptical. Sommerfeld showed 
that if we take into account the change of the mass of the elec- 
tron with its velocity (see next chapter, p. 25) the energy varies 
slightly with the excentricity. The difference is so small (for 
the Balmer lines the separation is only about one-fortieth of that 
of the D lines of sodium) that it cannot be detected in the ordi- 
nary spectroscope. But when the lines are examined with high 
dispersion it is seen that each really consists of several lines close 
together (' fine structure '), and Paschen, Wood, and others have 
shown that the separation of these components is exactly that 
required by Sommerfeld's theory. 1 

(Thus with these two spectra, that of atomic hydrogen and 
that of ionized helium, the Bohr theory is able to calculate the 
position of the lines in every detail, and with exact accuracy. ) In 
none of the more complicated cases, not even with neutral 
helium or molecular hydrogen, can the theory yet be applied in 
the same detail ; but jits success with the simpler spectra gives 

1 A still more recent refinement in the interpretation of the fine structure 
is referred to later, p. 84. 


Bohr's Theory of the Hydrogen Atom 

us confidence in its general truth ; and even with the m.' 
complicated spectra it affords the only explanation yet suggesl 
of their fundamental characteristics the series relationships 
the lines, the connexion between the arc and the spark spect 
and the whole character of the X-ray spectra from the origi: 
law of Moseley up to the most recent developments. ) 





. reached. 

* L 

dynamical problem becomes much more complicated 
_L when we Kave to deal with atoms containing several elec- 
trons, and it is not possible here to do more than describe the 
results, with a general account of the methods by which they are 

The first , question to be decided is what types of orbit are 
possible. ( On the simple Newtonian theory described above, the 
energy of the orbit is independent of the excentncity, and hence 
is the same for a circle as for a^ellipse. Sommerfeld however 
pointed out that since in an elliptical orbit the nucleus occupies 
one focus, the electron comes nearer to the nucleus at one part 
of its orbit, and therefore will move quicker. This must (on 
relativity principles) cause its mass to increase, and so it can be 
shown that instead of continuing to move on the ellipse, the 
electron will go a little farther round the nucleus each time : so 
that the whole (approximate) ellipse, or its major axis, will slowly 
rotate (Fig. 1). j The planet Mercury has a similar orbit, of which 
the perihelion moves forward 43 seconds of arc every century, or 
one complete revolution every 2-88 million years. This rotation 
of the ellipse is comparatively slow : with the hydrogen atom 
the electron traverses the ellipse some "40,000 times for every 
revolution of the major axis (with the planet Mercury the ratio 
is 12 millions to 1). 

Thus the motion of the electron is really made up of two 
motions superimposed on one another, a simple elliptical motion, 
and a slower rotation of this ellipse round the nucleus. It follows 
that just as we must quantize the angular momentum of the 
electron in the ellipse, so we must quantize that of the rotation 
(precession) of the ellipse itself : we shall have a definite series 
of degrees of ellipticity, just as we have a series of values of the 
total energy. In other words, the orbit must be characterized by 
two quantum numbers, the principal n and the subsidiary k. 1 

1 To avoid confusion from the different systems of notation employed, 
it should be observed that every orbit has an azimuthal quantum number 
n a and a radial quantum number n r : the total quantum number n is the 

306* jj 


The Bohr Theory of Atomic Structure 

As a rough approximation it may be taken that the principa 
quantum number represents the major and the subsidiary th< 
minor axis (more accurately the latus rectum). When the tw< 
are equal the orbit is a circle : when they are unequal it is ai 
ellipse, and the more they differ the more excentric the ellipse is 
With a nucleus of a given atomic number, all orbits of the sam< 
n have (as a first approximation) the same maximum diameter 
and all of the same k the same mmimum distance from th 

FIG. i 

nucleus. (All these statements need considerable modificatior 
in the case of atoms with large numbers of electrons.) The shape 
of the four possible orbits of principal quantum number 4 is 
shown (disregarding the precession) in Fig. 2. 

The second quantum number can obviously have any integral 
value up to but not exceeding that of the first, and so if the lattei 
is n there will be n possible kinds of orbit 1 n l9 n z , n 3 , . . .n n . 
Bohr's object is to determine the values in terms of these two 
quantum numbers of all the orbits (the number of which is equal 

sum of these two. In the ' n^ ' system of Bohr n is the total and k the 
azimuthal quantum number. Thus : 

n = n a + n r . 

k - n a 

n T = n k 

1 An n Q orbit is impossible, since it would be a straight line reaching the 

Types of Orbit 27 

to the atomic number) of the electrons in the ' normal ' atom 
of any element. By the normal atom he means an isolated 
atom of the element at a temperature at which it has ceased 
to radiate, and all its electrons have returned to their lowest 

Bohr's method is based largely on information afforded by the 
spectra of the elements, but also relies to some extent on the 
periodic table itself. We niay begin by considering the lightest 
elements. In hydrogen we have the simplest possible atom : 


FIG. 2 

there is only one electron, and this occupies a l x orbit. In 
helium with a rise of the nuclear charge to 2, a second electron 
is taken up, which also occupies a Ij orbit, probably in a plane 
inclined to that of the first. (There is also another (metastable) 
arrangement possible with helium, but that cannot be discussed 
now.) These two electrons in I : orbits (the K electrons) are also 
found in all the heavier elements ; this is proved by the validity 
of Moseley's law, that there is a constant relation between the 
frequency of the shortest X-ray line of an element and its atomic < 
number. This line is due to an electron returning to the K 
(1-quantum) group : if at any point in the series of elements this 
group expanded and admitted more than two electrons, the 
relation would change at that point. The third electron intro- 
duced in lithium must therefore occupy an orbit of a different 
type. Already in helium the second electron is to some extent 
affected by the repulsion of the first, which partially neutralizes 
the attraction of the nucleus. If a third were introduced into 

28 The Bohr Theory of Atomic Structure 

the 1-quantum group, the repulsion of the first two would be toe 
great for it to remain there, even with the increased nuclea] 
charge of 8. It therefore takes up an elliptical 2j orbit, ir 
which for one part of its path it is actually inside the orbits o 
the K electrons, and exposed to the full attraction of the nucleus 
for the rest of its course it is outside the orbits of these electrons 
which largely shield it from the nuclear attraction. While we 
can thus see a reason for the change in the type of orbit, we can 
not yet calculate the forces exactly enough to say why it occurs 
precisely at this point ; but both the spectroscopic and the 
chemical evidence show that it does so. The same may be saic 
of other conclusions of the Bohr theory, such as those given or 
p. 40. 

In lithium, then, the third electron occupies a much large] 
(2j) orbit than the first two, and the work of removal is far less 
as is proved by the ionization potential (the potential difference 
required to give an electron sufficient velocity to remove ar 
electron from the atom in the vapour) being only 5 volts 
whereas for helium it is 25 volts. It is evidently the present 
of this single easily removed electron which gives lithium iti 
univalent character ; and the identical change in propertiei 
which we find when we go from any other inert gas to its sue 
ceeding alkali metal shows that a corresponding change o 
structure occurs in every case. 

These conclusions indicate the important position which th< 
inert gases occupy in the periodic scheme. They mark the point; 
at which a quantum group has the number of electrons which i1 
requires for stability. It is to this that they owe their chemica 
inertness ; their stability is so great that it cannot be increasec 
that redistribution of electrons between atoms which con 
stitutes chemical combination. 

Now the atomic numbers of the inert gases show a remarkable 
regularity : 

He Ne A Kr Xe Em 

Atomic number .2 10 18 36 54 86 

Difference . 8 8 18 18 32 

They are all represented (Rydberg, 1914) by the expression 
2 (I 2 + 2 2 + 2 a + 3 2 + 8 2 + 4 2 ) taken to the necessary numbei 
of terms. This is a very striking fact. It reveals an unsuspected 
symmetry in the periodic table, far more remarkable than the 
rather forced arrangement in periods of 8 to which we are 

I by 

Application to the Periodic Table 29 

accustomed. It is particularly to be noticed that the emanation, 1 
which complies with the formula, lies beyond the confusing group 
of the rare earth metals, which are thus shown to form a per- 
fectly regular part of the whole symmetrical table. 

The results further indicate that the size of a stable group of 
electrons is always of the form 2n z , being 2, 8, 18, 32, and that 
the successive periods of the table, each ending in an inert gas, 
are due to the building up of these groups. At least it is evident 
that as we proceed along the first short period from helium to 
neon we are building up a group of eight 2-quantum orbits 
(2! ellipses and 2 2 circles), and that in neon this group is com- 
pleted, and hence we have an element that is stable and 
chemically inert. The further development of the periodic table 
can be deduced either from the physical or from the chemical 
properties. The latter method was adopted by C. R. Bury, 2 
who arrived independently at the same general conclusions as 
Bohr reached on physical grounds. The chemical argument may 
be given first, as establishing the main lines of development of 
the structure, although for the details we have to rely on the 
physical considerations advanced by Bohr. 

If we disregard the smaller details of the periodic table, its 
general characteristics can be described, without reference to 
atomic structure, as follows. After hydrogen and helium we 
have the eight elements from Li 8 to F 9 and Ne 10 with a definite 
succession of properties. The second short period, containing 
the eight elements from Na 11 to Cl 17 and A 18, shows the same 
kind of development. After argon we have a period of eighteen 
elements up to krypton 86. This starts with potassium and 
calcium along the same lines as in the two preceding periods ; 
but the following elements, although they have some resem- 
blances to the corresponding members of the first two periods, ( 
go more and more off the lines, until we find the place of the / 
eighth element, where we should expect an inert gas, occupied 
by the triad Fe, Co, Ni, to which there is no analogy among the : 
earlier elements. This triad is followed by a series of eight, Cu, 
Zn, . . . Br, Kr, which, at any rate after the first member, show 
a close resemblance to the first group of eight. In the second 

1 The names radon, thoron, and actmon are now accepted for the three 
isotopic emanations. It is desirable that there should be some name for 
element no. 86 irrespective of any particular isotope, and I have retained 
the name emanation (with the symbol Em) for this purpose. 

2 Journ. Amer. Chem. Soc. 1921, 43, 1602. 


30 The Bohr Theory of Atomic Structure 

long period (Rb . . . Ru, Rh, Pd : Ag . . . I, Xe) we have th< 
same behaviour repeated. 

In the next (very long) period of thirty-two we again start 01 
normal lines with Cs, Ba : but we then find in La 57 to Lu 71 ai 
entirely new kind of group, of fifteen successive elements th< 
rare earth metals all trivalent and all very similar. The fol 
lowing elements Hf 72 to the triad Os, Ir, Pt 78 are just like th 
middle elements of the two long periods, and are followed by i 
group of eight (Au 79 to Em 86), which resemble the two shor 

These relations suggest that the obvious idea that the orde 
of the groups in the atom is the order of the successive incre 
ments from one inert gas to the next (and that emanation, fo 
example, has the structure 2, 8, 8, 18, 18, 82) is wrong. If it wer< 
correct, we ought to get a wholly different type of developmen 
according to the size of the group which was being built up. Ii 
particular, we should not find as we do, that the type of growtl 
in the first two short periods is repeated later in the seven ele 
ments preceding each inert gas. Now in the first short perioc 
we know that this is due to the building up of a group of eigtr 
electrons in orbits of the highest quantum number in the atom 
We may conclude that the same thing happens at the close of th< 
longer periods : that every inert gas has an outer quantun 
group of 8, and that krypton, for example, is not (2) (8) (8) (18) 
but (2) (8) (18) (8). If this is so, we must have in the first long 
period, which represents the passage to this structure of kryptor 
from that of argon (2) (8) (8), not the formation of an externa 
(4-quantum) group of 18, but the growth of the third quanturr 
group from 8 to 18, followed by the formation of a new fourtt 
quantum group of 8 (this is not exactly true, but we are no-vi 
dealing only with the main outlines of the process). We car 
also see why there are ten elements instead of eight in the firsl 
section of the long period (from K 19 to Ni 28, at the end of the 
triad), smce 188 = 10. The same thing must occur agair 
in the second long period : the 4-quantum group of 8 expands 
to IS^d 44B), and then a 5-quantum group of 8 is added, giving 
Xe as (2) (8) (18) (18) (8). In Em 86 we must again have the 
largest group in the middle, and an outer group of 8, giving (2) 
(8) (18) (82) (18) (8). The expansion of the fourth quantum 
group from 18 to 32 is a new phenomenon, involving fourteen 
elements : this is no doubt the cause of the unique series of rare 
earth metals from La 57 to Lu 71. 

Application to the Periodic Table 31 

These conclusions, which were also arrived at on the physical 
evidence by Bohr, give us as the foundation of the table the 
following structures of the six inert gases : 

Quantum Group .1 2 8 4 5 6 

He 2 . . .2 

Ne 10 . . .2 8 

A 18 . . .2 8 8 

Kr 86 ... 2 8 18 8 

Xe 54 . . .2 8 18 18 8 

Em 86 . . 2 8 18 82 18 8 

The fundamental principles of this system are two. (1) The f 
maximum number of electrons that a group can contain is 2 n z , 
where n is the principal quantum number. But the groups 
attain a state of comparative stability when they have eight or 
eighteen electrons, even if they are capable of holding eighteen or 
thirty-two. (2) In the stable structures of the inert gases the 
largest groups tend to be those of the middle quantum numbers, 
and the highest quantum group is always eight. 

" Before we discuss the structures in detail, we have to consider 
a recent development of the Bohr theory affecting a question 
which has not yet been raised, the distribution of the electrons 
of a group among the subgroups. 1 Bohr originally assumed that 
in a completed group the electrons were equally distributed 
among the subgroups : thus for the stable numbers 8, 18, 32 the 
arrangements were : 

Orbits . n-L n z n z n^ 

4 4 = 8 

6 6 6 = 18 

8 8 8 8 = 82 

The maximum number of electrons in a group being 2 n 2 , and of 
subgroups n, it followed that the maximum number of electrons 
in a subgroup was 2n. This conclusion was based on general 

1 A group means all the electrons in an atom whose orbits have th| same 
principal quantum number , the term ring, which is often used instead, is 
less suitable because it suggests that the orbits of different groups are quite 
separate from one another, whereas in fact they are largely inter-penetrat- 
ing. A subgroup consists of the orbits of the same principal and subsidiary 
quantum numbers. For the electrons whose orbits also have the third 
quantum number (discussed below) the same, we may use Andrade's term 
' grouplet '. 

32 ' The Bohr Theory of Atomic Structure 

principles of symmetry. Later work has shown that it need! 
modification. While the subgroups retain the meaning and im 
portance which Bohr assigned to them, a different distributior 
of the electrons between them must be adopted. This is primarilj 
due to the discovery that for a complete specification of th< 
orbits two quantum numbers are not sufficient, but a third musl 
be introduced. The most direct evidence of this is derived frorr 

v/a study of the X-ray absorption spectra. These differ from the 
' optical ' absorption spectra in one important respect, whic? 
needs a few words of explanation. 

When a beam of radiation falls on an atom it will, if ifc^fre- 

/ quency, and therefore its quantum, is large enough, disturBroVie 
or more electrons from their orbits, and drive them into outei 
orbits, or even away from the atom altogether (ionization) ; the 
process is in general the reverse of that of light-emission, which 
we considered in the last chapter. This expenditure of energy 
causes the removal from the beam of the radiation of a particular 
wave-length, and an absorption spectrum is produced. X-rays 
differ from ' optical ' radiation a term used to cover the infra- 
red, visible and ultra-violet only in degree, being of much 
shorter wave-length, mostly from 10 to 0-1 A.U., while the opti- 
cal spectrum ordinarily measured is from 100,000 to 1,000 A.U., 
intermediate wave-lengths (1,000-10) being much more difficult 
to measure (1 A.U. = 10~ 8 cm.). The X-ray quanta are pro- 
portionally larger, and are able to remove the firmly bound 
innermost electrons of an atom, while the optical spectra corre- 
spond to the energies required for changes in the most loosely 
attached electron of the outer group. Thus the ordinary optical 
absorption spectra of gases are due to the shifting of these outer 
electrons to still more distant orbits, and as every such shift 
involves a definite expenditure of energy, the spectrum consists 
of a series of dark lines. (In a liquid or solid these lines are 
broadened out into bands, through the disturbing influence of 
the electric fields of neighbouring atoms.) The X-ray absorption 
spectrum is of a different form. If the radiation is hard enough 
(i.e. of short enough wave-length) to displace an electron from 
one of the inner groups in a heavy atom., this cannot go to a 
neighbouring group, because all these are full : it must either 
go to the outermost group or leave the atom entirely ; and the 
difference between these two shifts is scarcely measurable. 
Hence, when atoms are struck by ' white ' X-ray radiation 
(radiation having a continuous spectrum) absorption only begins 

The Third Quantum Number 33 

when we reach a frequency great enough to expel the electron. 
But the rather harder radiation beyond this is also able to expel 
the electron, and the excess of its quantum over the energy re- 
quired for the expulsion is taken up by the electron in the form 
of kinetic energy. If the wave-length is shorter still, the electron 
is again expelled, with a greater velocity. Thus instead of a 
sharp line we get in the absorption spectrum a band with a sharp 
edge at the point where the energy becomes just sufficient for 
the removal of the electron in question. This is what is meant 
by the ' absorption edge ' of such a spectrum. By measuring 
these edges for the inner group of a heavy atom we can deter-l 
rnnfjfe the work needed to remove electrons from every kind of 
orbit in the completed groups : the values so obtained are called 
the energy levels of the atom : they correspond to the ' spectral 
terms ' of the optical spectra. 

On the original Bohr theory the number of energy levels for 
every group must be identical with the number of subgroups, 
and hence equal to the principal quantum number. But on 
examination it is found that the actual number is larger than 
this. In the first (K) group there is only one level, as the theory 
requires, but in the second (L) there are three instead of two 
(2 1} 2 2 ), in the third (M) five instead of three, and in the fourth 
(N) seven instead of four : in fact the number of kinds of orbits 
in the nth quantum group is not n, as the theory requires, but 
2n - I. 1 

Thus it is clear that the Bohr (n k ] system, with its two quan- 
tum numbers, is insufficient to account for the variety of orbits 
which actually occur, and that a third quantum number j must 
be introduced and an n kj system adopted. The physical meaning 

1 As an illustration, the following list of the energy levels of uranium is 
quoted from Siegbatm. They are expressed in terms of v/R, and so are 
proportional to the energy of removal (the P levels are too close together to 
be differentiated). 

Group . . . 1 (K) 2 (L) 3 (M) 4 (N) 5 (O) 6 (P) 
No. of electrons in 

group ... 2 8 18 32 18 12 

Energy levels, v/R . 8477 1608 5 408-3 106 6 23 9 1-7 






















34 The Bohr Theory of Atomic Structure 

of this third number is not yet clear : but it must be remembered 
that the accuracy of spectroscopic data is so great that it is legiti- 
mate to introduce a term of this kind if it enables us to calculate 
the results quantitatively, even if we cannot give it a physical 
interpretation. Whatever j is, it is something which can never 
have more than two values for any given values of n and k. It was 
originally suggested that it represented the orientation of the orbit 
with respect to the axis of angular momentum of the atom as a 
whole, Recently, however, Sommerfeld and Unsold x have sho\wi 
that the introduction of a third quantum number makes it pos- 
sible to explain in every detail the fine structure of the spectra of 
atomic hydrogen and ionized helium, including the occurrence of 
lines apparently forbidden by the correspondence principle, 2 the 
relative intensities of the lines, and their behaviour in a magnetic 
field (Paschen-Back effect). Since therefore j holds for a system 
of a nucleus and a single electron, it cannot depend on the 
orientation of electronic orbits. A more probable suggestion, 
favourably regarded by Bohr, is that it represents the direction 
of spin of the electron round its own axis. 3 

Whatever the meaning of j, it must, in order to account for the 
observed atomic levels, have two values for every n k subgroup 
except those in which k = 1. A scheme of distribution of the 
electrons among these levels was suggested in 1924 independently 
by Main Smith 4 and by Stoner, 6 the former basing it chiefly on 
chemical arguments (which however are very difficult to 
follow), and the latter on physical evidence derived from the 
spectra and the magnetic properties. The necessary number of 
levels is obtained by following the rule that j is either equal to 
k or is one less. We thus get in any Nth quantum group a 
series of levels N u : N ai , N aa : N 32 , N 38 : N 48 , N 44 : &c., in 
which the colons mark off the Bohr nj. subgroups. If we make 
one further assumption, that the maximum number of electrons 
in any level is twice the third quantum number, the size of 
the Various quantum groups is accounted for, since we have : 

1 Z.f. Physik, 1926, 36, 259. ~~ 

* This principle of Bohr's is a limitation of the number of transitions 
possible among the orbits of an electron. In particular it requires that in, 
every transition k should change by 1. It was originally derived from 
a * correspondence ' between the results of classical and quantum dynamics. 

a Uhlenbeck and Goudsmit, Nature, 1926, 117, 264 ; Bohr, ibid. See 
also Eddington, Richardson, Lindemann, and Frenkel, ibid. 652-4. 

* Chemistry and Industry, 1924, 48, 828. 
s PlnL Mag. 1924, 48, 719. 

The Stoner-Main Smith Distribution 35 

Level N n N 21 N 22 N 32 N 83 N 43 N 44 

Maximum number 2 24 46 68 

N - 1 2 __ __ _ = 2 

N=2 2 24 _____= 8 

N = 3 2 24 46 _ =18 

N = 4 2 24 46 68= 32 

n ft subgroups 26 10 14 

classification is in entire agreement with the optical and 
X-ray data, those transitions alone occurring in which k changes 
by 1, and j either changes by 1, or remains unaltered. 

It will be seen that this scheme, which is now generally 
accepted, retains the Bohr n k classification, but carries out a 
further subdivision. It appears that the importance of this sub- 
division is less than that of the Bohr subgroups : levels differing 
only in the third quantum number are less easy to distinguish, 
and it is not yet possible to say how many of the orbits of an 
incomplete n k subgroup belong to each of the two n^ levels 
(' grouplets '). Hence the essential correctness of the Bohr 
classification is maintained, but with two important modifica- 
tions. Firstly, the number of electrons in each subgroup is 
different : in place of (4, 4), (6, 6, 6), (8, 8, 8, 8), we have (2, 6), 
(2, 6, 10), (2, 6, 10, 14). Secondly, the development of the groups 
in the periodic table acquires rather a different significance : 
whereas Bohr supposed, for example, that the two subgroups 
of 4 in the fourth quantum group in krypton expanded to (6, 6, 
6) in xenon, and to (8, 8, 8, 8) in emanation, we now have to 
realize that the grouplets present in the lighter atoms still persist 
in the heavier, and that the grouplets 2x4 n + 2x4 21 + 4 
x4 2a which occur in krypton are still present in xenon and 
emanation, though with the addition first of 4 x 4 32 + 6 x 4 33 , 
and then of 6 x 4^ + 8 x 4 44 . This applies particularly to the 
pair of electrons of N,i orbits, which was not recognized by Bohr 
except in the first quantum group : this pair, which in helium 
(N = 1) constitutes an absolutely complete group, recurs on the 
new scheme at the beginning of all the other groups, and we 
shall see that it can under suitable conditions acquire, even in the 
groups of higher quantum number, something of the stability 
which it possesses in helium. 

Before we consider the application of these principles to indi- 
vidual elements, something must be said of the peculiarities of 
the optical spectra, from which so much of the evidence for the 

36 The Bohr Theory of Atomic Structure 

atomic structures is derived. The lines of the optical spectrum 
are due to the return of the most loosely bound electron in the 
atom from a higher (excited) orbit to a lower, and their frequency 
is proportional to the difference of energy of the two orbits. The 
same atom can give different spectra according to the means 
adopted for exciting it, and these are known as arc and spark 
spectra. In the arc the excitation is due to the high temperature, 
and the consequent collisions of the rapidly moving atoms with 
one another : these drive the outer electrons into higher quan- 
tum orbits, but as a rule do not detach them from the atom. 
t/llence the radiation is due to neutral atoms. In the spark th 
energy is communicated to the atom mainly by swiftly moving 
electrons ; these are capable not only of exciting the neutral 
atoms, but also of removing one or more electrons from them 
completely of ionizing them and then of further exciting the 
ions so produced. The spark spectrum thus contains other lines 
(spark lines or enhanced lines) produced by these ionized atoms. 
The spectrum of a neutral atom X is known as X I, that of the 
atom X+ which has lost one electron as X II, that of X K + as 
| X III, and so on. 

Now an excited atom, in which one electron has been driven 
into a higher quantum orbit, a large part of which is far removed 
from the nucleus and the other electrons, has a certain resem- 
blance to a hydrogen atom. The excited ' optical ' electron is 
under the influence of the nucleus with its charge of + N units 
surrounded by N -1 electrons (where N is the atomic number) - 
when it is in the outer parts of its orbit, these are relatively at 
about the same distance from it, so that their effect is approxi- 
mately equivalent to that of a single positive unit. It is for this 
reason thatthearc spectra of other elements can berepresented by 
formulae resembling (especially for the terms of higher quantum 

conn R T 

constant R. If, however, the 

to an atom 


Nature of Optical Spectra 37 

These considerations apply as a first approximation only, and 
the spectra of individual elements all have their own peculiari- 
ties, which are often very complicated. In particular, the lines 
tend to occur in close ' multiplets ' sets of 2, 3, or more the 
number being constant in a given spectrum, or at least in a given 
spectral series. The degree of multiplicity, the cause of which 
cannot be discussed here, is closely related to the position of the 
elements in the periodic table, the arc spectra of .the alkalis 
giving doublets, and those of the alkaline earths triplets, and 
generally the odd periodic groups giving even multiplicities, and 
vice versa. When a spark spectrum is exammed it is found that 
it closely resembles the arc spectrum of the preceding element, 
if allowance is made for the change in the constant : thus the 
spark spectrum of magnesium (Mg + ) is like the arc spectrum of 
sodium, but with the frequencies about four tunes as great, and 
while the arc spectrum of magnesium contains triplets, its spark 
spectrum, like the arc spectrum of sodium, contains doublets. 
The process has been carried farther : under more intense ex- 
citation it is possible to remove more electrons, and obtain 
the spectra of doubly and trebly ionized atoms 1 (Fowler, 
Paschen) ; and the rule still holds that the spectrum resembles 
that of the neutral atom with the same number of electrons, 
allowance being made for the increased constant S 2 R. Thus we 
get the following series, in which the vertical groups represent 
similar spectra : 

Electrons. 11 , 12 13 14 

Doublets, i Singlets Doublets. Singlets 
and triplets. and triplets. 

Al Si 








This rule, which is known as the spectroscopic displacement law 
of Kossel and Sommerfeld, illustrates the principle of atomic 
number (an increase of one as we pass from one element to the 
next in the table) for the planetary electrons in the same way 

1 The spectra of even more highly ionized atoms (up to Cl VII i e. with 
6 electrons removed) have been obtained by Millikan and Bowen by the 
' hot spark ' method, in which the pressure is reduced below 10- 3 mm., so 
that a high voltage produces only very short sparks (201 mm.) of very 
great intensity. 

38 The Bohr Theory of Atomic Structure 

as the radioactive displacement law of Russell, Fajans, and 
Soddy (p. 7) does for the nuclear charge. It is important from 
other points of view as well. It emphasizes the remarkable 
stability of the atomic structures, which are seen to retain their 
form even with considerable variation of the strength of the 
positive field in which the electrons move. This stability is one 
of the most marked characteristics of the atom, and the physical 
theory cannot as yet fully account for it. Of equal importance 
is the fact that in certain parts of the periodic table the displace- 
ment law no longer holds : certain electronic structures are 
possible only with particular values of the nuclear charge. This 
occurs at those points at which a development of a quantum 
group from one stable form to another (from 8 to 18, or from 
18 to 82) is beginning, where it can be shown that the arrange- 
ment of a given number of electrons is changed when the nuclear 
charge is increased. The direction of the change is always the 
same : the increase of the atomic number brings the electron 
into an orbit of lower principal quantum number and greater 
excentricity (e.g. from 4^ to 3 3 ). The cause of this change will 
be further discussed under scandium (below, p. 40). The spec- 
trum evidence in this way affords a valuable proof of the exact 
t point in the series of elements at which the development of the 
quantum group begins. 

We may now consider the application of these principles to the 
periodic table 1 in more detail. The simplest method is to take the 
elements in the order of the atomic numbers. Hydrogen (1x1 n ) 
and helium (2xl 1:L ) have already been discussed. In the next 
two elements (Li 3, Be 4) the spectra show that first one and then 
two electrons in 2 n orbits are added, so that in beryllium the 
2 n subgroup is full, and it remains unchanged in all subsequent 
elements. That the last electron in boron (5) cannot occupy the 
same subgroup as the previous two was concluded by Bohr on 
the analogy of aluminium, for which the spectrum shows that 
one of the three electrons in the highest quantum group is in a dif- 
ferent kind of orbit from the other two : this has since been proved 
spectroscopically for boron, and is now, of course, a necessary 

1 The general relations are shown in the periodic table given on p. 89, 
which is taken from Bohr. The frames enclose elements in which the inner 
group is in a state of incomplete development : the lines connect elements 
which have their imperfect groups of the same size. The rare earth metals 
between Pi 59 and Yb 70 are omitted for convenience. The electronic 
structures of individual elements, according to the most recent results, are 
given on p. 48. 

The Periodic Table 


consequence of the classification of Stoner and Main Smith : 
the fifth electron must occupy a 2 2 orbit of one or other kind. 
The succeeding elements C, N, O, F have respectively 2, 8, 4, 



Li Be B C N O > Ne 

3 4 S 6 7 8 9 IO 

Z Ca 

19 2O 

Rb Sr 

37 38 

Sc Ti V 

21 22 23 

Cr MnFe Co "Mi 

24 25 26 27 28 

Zn Ga Ge ;As Se Br Kr 

29 30 31 38 35 34 35 36 

Zr NbMo Ma Ru Rh Pd A 

40 41 4g 43 44 45 4? 4 

Cd In Sn Sb Te 

48 49 50 51 52 

AuHgTIPb Bi Po -Em 

79 80 81 82 83 84 85 88 

- Ra Ac' Th Pa U 

87 88 89 90 91 92 

and 5 electrons in the 2 21 and 2 22 levels, though we cannot be 
sure how they are distributed between them. In neon (10) these 
levels are full, with 2 in 2 21 and 4 in 2 22 . The second quantum 
group has now received the largest number of electrons that it 
can hold, and no subsequent change occurs in it. 

In the second short period (Na 11 to A 18), the same process of 

40 The Periodic Classification 

development is exactly repeated in the third quantum group. 

We thus reach argon, which is (2) (224) (224). 

In the next period we begin as before by adding first one and 
then two electrons (in K 19 and Ca 20) to the new (fourth) group, 
so that up to this point (with a nuclear charge of 20) the third 
quantum group remains imperfectly developed, with the 8 8 sub- 
group unoccupied. But this must soon begin to fill, and Bohr 
has pointed out the exact place at which this happens. In the 
arc spectrum of potassium we have a measure of the energy 
differences of the various possible orbits of the nineteenth (last 
added) electron, moving round a nucleus of charge 19. From 
this we can deduce that it is about twice as firmly bound in a 
4 X as in a 3 3 orbit. In the spark spectrum of calcium (singly 
ionized) we are again dealing with the nineteenth electron, but 
now the nuclear charge is 20. Here we find that the electron is 
only very slightly more firmly bound in a 4j than in a 8 3 orbit. 1 
It is evident that if we could measure the spectrum of doubly 
ionized scandium (19 electrons, nuclear charge 21), we should 
find that the 8 3 orbit was more stable than the 4^ Hence the 
expansion of the third quantum group must begin with scandium, 
which will have two 4, electrons and one 3, all three however 

* o 

much more loosely held than the remaining eighteen. The reason 
for this change of orbit of the nineteenth electron can be given in 
general terms. The previous eighteen are arranged in an argon 
structure. When the nuclear charge is 19 (K), the positive field 
outside these eighteen is comparatively weak, as their screening 
effect neutralizes nearly the whole of the attraction of the 
nucleus : hence the electron is drawn into a long elliptical orbit, 
for part of which it comes into the powerful field close to the 
nucleus. A rise in the nuclear charge to 20 (Ca) increases the 
strength of the field near the nucleus by 5 per cent., but nearly 
doubles that of the external field. Thus there is much less differ- 
ence between the field inside the argon group of eighteen elec- 
trons and that outside in calcium than in potassium, and still 
less in scandium. A point will, therefore, be reached at which 
a circular 3 3 orbit lying wholly outside the orbits of the first 
eighteen electrons becomes more stable than a 4 l9 which pene- 
trates far inside them : and the spectra show that this point is 
reached in scandium, where the nuclear charge is 21. On the 
other hand the screening effect of this nineteenth electron 

1 See Bohr, Theory of Spectra, p. 102, where diagrams of the spectra are 

Transitional Elements 41 

weakens the field outside its own circular orbit, so that the subse- 
quent (twentieth and twenty-first) electrons in scandium will 
again occupy long 4 X orbits. 

In the following elements up to zinc (30) there is no reason to 
think that any increase in the fourth quantum group beyond 
two takes place ; indeed it is probable that in some (Cr and Cu) 
it is reduced to one. The elements from scandium (21) to nickel 
(28), which according to Bohr have not only the outermost but 
also the next quantum group incomplete (and which are dis- 
tinguished in the table, p. 39, by being enclosed in a frame), 
have remarkable properties both physical and chemical. With 
the exception of scandium, of which the (trivalent) ion should 
properly stand outside the frame, they all have variable valency, 
their ions are coloured and are paramagnetic, and they all have 
a marked catalytic power. The variable valency obviously 
depends on the fact that the work required to detach one or 
more of the 8 3 electrons is not so much greater than that needed 
for the 4-t electrons but that it can be effected by chemical 
agencies : so that the number of electrons which can serve for 
valency purposes can be varied. The colour also results from the 
incompleteness of the group. A coloured ion is one which ab- 
sorbs light of the visible spectrum, and hence it must be capable 
of an electronic transition of which the energy corresponds to a 
quantum of visible light something between 40,000 and 70,000 
calories per gram-atom. In an ion Like Na + or Ca ++ , where the 
outer group is complete, the only possible transition is to a 
higher group, but to transfer an electron from a completed group 
to another would consume far more energy, and cause absorption 
in the ultra-violet. This is illustrated by the behaviour of 
sodium. ' The metallic vapour, in which the atom retains its 
valency (3j) electron, is coloured : it absorbs in the yellow (the 
D line), owing to the transition 3 X -> 3 2 . But the sodium ion, 
from which the valency electron has been removed, and in which 
only the very stable complete groups (2) (8) remain, is colourless. 
The simple ions of the metals from titanium to nickel all contain 
an incomplete third quantum group, and hence allow of transi- 
tion from one level of this group to another, in which the absorp- 
tion of energy is small, and causes absorption in the visible 
spectrum. The paramagnetism of these ions is due to similar 
causes, though we do not know so much about them. The ions 
with completed groups are diamagnetic because the magnetic 
moments of the various orbits balance one another ; but where 

42 The Periodic Classification 

the group is imperfect this balance is not attained. The catalytic 
properties, which are equally well marked, are presumably con- 
nected with the variation of valency. 

These properties also enable us to determine where the deve- 
lopment of the third quantum group is complete. Copper (29) 
has one more electron than is required to complete this group. 
The cuprous ion might therefore be either (2) (8) (17) 1 or 
(2) (8) (18). That it has the latter structure, with the third group 
complete, is proved by its being colourless and diamagnetic. On 
the other hand the eighteen group in this atom, with a nuclear 
charge of 29, is not so firmly held that it cannot be broken into 
by chemical forces, and the cuprous ion can be converted into 
the cupric Cu ++ = (2) (8) (17). Here we have the incomplete 
group again, and the colour and the paramagnetism reappear. 
In the next element zinc (80) the increased nuclear charge holds 
the eighteen group too firmly for it to be broken into, and accor- 
dingly zinc is always divalent, colourless, and diamagnetic. 

Thus the general development of the series Sc 21-Zn 30 is 
clear, and the beginning and end of the transition are sharply 
defined. The question whether there are always two electrons 
in the fourth group has been disputed : the answer depends on 
the spectrum evidence. The most recent work 1 confirms Bohr's 
view that there are two, except in chromium, where there is 
probably only one. In copper the arc spectrum shows mainly 
the lines of an atom (2) (8) (18) 1, as we should expect from the 
existence and properties of the cuprous ion, but there are also 
lines which indicate the presence of atoms (2) (8) (17) 2 in equili- 
brium with the others. 

The remaining elements from Zn (30) to krypton (36) have the 
same relations as those of the first two short periods. 

In the second long period (K-Ag-I, Xe) the development re- 
sembles that of the preceding period, though not quite so closely 
as was at first supposed. In Rb 87 and Sr 38 we have as we 
should expect one and two electrons in the new (fifth) group, and 
in Y 39 the fourth group begins to expand. But there is evidence 
from the spectra 2 that the imperfect eighteen group is more 
stable when the principal quantum number is 4 than when it is 8 : 
and in particular that while Fe is (2) (8) (14) 2, Ru is (2) (8) (18) 
(15) 1, and while in nickel it is clear that two electrons are lacking 
to the eighteen group, the arc spectrum of palladium makes it 

1 Grimm and Sommerfeld, Z. /. Physik, 1926, 36, 36 ; Somraer, ibid. 
37, 1. a See Sommer, loc. cit. 

Rare Earth Metals 43 

probable that in the ' normal ' atom this group is complete : 
Pd 4$= (2) (8) (18) (18). At what stage one of the two fifth 
quantum electrons which must be present in strontium is recalled 
to the fourth group is uncertain : according to Sommer this 
must happen at least by the time we reach zirconium. The 
greater stability of the eighteen in the fourth quantum group is 
shown by the behaviour of silver : this, as we know, differs from 
its analogue copper in that the eighteen group cannot be broken 
into by chemical means at all : it invariably gives a univalent and 
colourless ion. According to Grimm and Sommerfeld (loc. cit.) 
the removal of an electron from the eighteen group requires at 
least 40,000 calories more (per gram-ion) with Ag + than with Cu + . 
In the next (rare earth) period the relations are more compli- 
cated. We start with Xe 54 = (2) (8) (18) (18) (8), and three 
processes occur during the period, the development of the fourth 
quantum group from 18 to 32, of the fifth from 8 to 18, and the 
formation of a new sixth quantum group of 8. We begin as 
before with the establishment of the N u pair in the sixth group 
(Cs 55, Ba 56) : then the fifth quantum group of 8 opens : La 57 
= (2) (8) (18) (18) (2, 6, 1) 2. With the next atom Ce 58 the 
fourth group opens, giving (2) (8) (18) (2, 6, 10, 1) (2, 6, 1) 2. In 
the succeeding elements the new electrons all go to this 4 4 sub- 
group, until it is completely filled at Lu 71 = (2) (8) (18) 
(2, 6, 10, 14) (2, 6, 1) 2. Throughout the whole of this series of 
rare earth metals, from La 57 to Lu 71, the fifth and sixth quan- 
tum groups remain unchanged at (2, 6, 1) 2 : the only change 
of structure is the growth of the 4 4 subgroup of 14 (6x4^ + 
8 x4 44 ). There is thus a very close similarity of properties 
(since the only change is far down in the atom), such as we find I ' 
nowhere else in the table. The elements are all trivalent, giving 
an ion (2, 6). It is however to be noticed that as the first 
occupants of a new type of orbit are usually more easily removed 
than the later ones, Ce 58, which has one 4 4 electron, can lose 
this and become quadrivalent, and Pr 59, which has two, can 
lose one of them m the same way, though less easily than cerium. 
The ions of the rare earth metals are paramagnetic (some very 
highly) and coloured. The colour is of quite a different type to /j 
that of the transition elements of the two preceding periods :[! 
instead of broad bands of several hundred A.U. the solutions 
give narrow absorption bands or lines, often not exceeding 
10 A.U. in breadth. This is strong evidence in favour of Bohr's 
view that the developing group in these elements is far down in 

44 The Periodic Classification 

the atom. The broadening of the absorption lines of an ion in 
solution is due to the electric fields of neighbouring atoms, which 
break up each line into components, whose separation depends 
on the strength of the field (Stark effect) : as the different ions 
present are thus affected in various degrees, the result is to spread 
the sharp line into a band. The broadening will obviously 
be greater, the more the orbits in question are exposed to the 
fields of neighbouring atoms ; and hence it is less in the rare earth 
metals, where these orbits are in an inner group, shielded from the 
influence of other atoms, than in the previous periods, in which 
the imperfect quantum group is the outermost group of the ion. 
In lutecium (71) the fourth quantum group is full, and hence 
in hafnium (72) the new electron must go to the fifth group, 
giving the structure (82) (2, 6, 2) 2. Thus if the theory is 
sound, the trivalent rare earth metals should stop at 71, and 72 
should be an element of the fourth periodic group, with a valency 
of four. If this were not so, it would mean that the whole scheme 
was at fault ; and it would be a unique case of a rise of valency 
of two units in going from one element to the next (from 72 to 
quinquevalent tantalum 78), indicating that an electron became 
less firmly bound when the nuclear charge increased, whereas 
the reverse must always happen. Hence the importance at- 
tached to determining whether 72 was a rare earth (trivalent) 
element or an analogue of zirconium : it was ultimately proved 
to have an extraordinarily close similarity to zirconium. In the 
following elements (Ta, W, Re, Os, IT, Pt) we have the same kind 
of development as in the transition elements of the two long 
periods : but the work of Sommer and others indicates that the 
resemblance is to the first rather than the second of these (V-Ni 
and not Nb-Pd), and that these elements have two electrons in 
the outer quantum group. This is supported by the behaviour 
of gold, in which, as in copper but not silver, some of the elec- 
trons of the penultimate 18 group can be utilized as valency 
electrons. Why this should be true of two electrons in gold and 
only one in copper-in other words, why copper has valencies of 
one and two, and gold of one and three is not yet known 

In the elements from gold (79) to emanation (86) we have the 
normal type of growth of the outer^groy^of eight. All the 
elements after mercury (80) have radioactive isotopes, and after 
bismuth (88) all the isotopes are radioactive. .Hence the absence 
r of elements 85 (efca-iodine) and 87 (eka-caesium) is probably due 
to instability of the nucleus. 

Four Types of Atoms 45 

The last period (Ra, Ac, Th, Pa, U) might be expected to be 
parallel to the rare earth period, the fifth group beginning to 
develop at 90 (Th). It is clear however from their properties, 
and especially from the continuous increase of valency up to the 
last member, that this is not so ; the increase of valency would 
cease (as it does with cerium) when the expansion of the 18 group 
began. These elements must resemble the first or second long 
period, and all the electrons added after emanation must go to the 
sixth or seventh quantum group. The first two electrons (in Ra) 
will clearly go to the seventh. Whether in Ac-U we have as in the 
first long period two, or as apparently in the second, only one 
electron in the outermost group, is uncertain, as the spectra of 
these elements have not yet been worked out. Sommer (loc. cit.) 
considers it probable, on the analogy of the earlier periods, that 
there is only one. 

To sum up the results of this physical investigation it will be 
seen that Bohr recognizes four different types of atoms. " 

1. Those in which all the electronic groups are complete (this 
word being applied to the subordinate stable numbers such as 
8 and 18, as well as to the absolutely complete numbers of 2n 2 ). 
These elements form no compounds : they are the inert gases. 

2. Those in which all but the highest quantum group are com- 
plete. These include the first two short periods, the elements up 
to seven places before and two after each inert gas, and generally 
all those which are not included in frames in the Bohr periodic 
table, p. 39. These elements have a fixed number of valency 
electrons, 1 and their simple ions are colourless. 

3. Those in which the two outermost electronic groups are 
imperfect (in the wider sense given above under (1)) : these are 
enclosed in a single frame. They show valencies varying by single 
units, are markedly catalytic, and form coloured and paramagnetic 
ions. These may conveniently be called the transition elements ; 
this term has commonly been limited to the triads with which 
each series concludes, but now that we recognize that these 
triads are not peculiar, but are only the final stages of a process 
extending over the preceding elements as well, the designation 
may be extended to the whole series. 

1 This does not necessarily mean that the value of the valency as ordinarily 
expressed is constant ; but it implies that this value, properly understood, 
normally changes only by 2 units at a time. The ' proper understanding ' of 
these relations is the main object of the succeeding chapters, in which certain 
real and apparent exceptions to the ' even number rule ' are discussed. 


The Periodic Classification 

4. Those in which the three outermost groups are imperfect 
(double frame) ; these are the rare earth metals. They resemble 
class 3 in some respects (especially in colour, paramagnetism, 
and catalytic power), but are unique in constituting a long series 
of elements all of the same valency, and all very similar in 

The list of atomic structures on pp. 48-50 summarizes the 
results of these investigations, in accordance with the latest 
spectroscopic data : I am much indebted to Dr. E. C. Stoner 
for help in compiling this. 1 It cannot be regarded as final, since 
some of the details, especially as to the number of electrons in 
the highest quantum group in the transitional elements, are still 

1 For the recent developments of the theory relating the structure to the 
spectral terms, see Heisenberg, Z.f. Phys. 1925, 32, 841 ; Hund, ibid. 33, 
343 ; R. H. Fowler and Hartree, Proc. Roy. Soc. 1926, 111, 88. A clear and 
comparatively simple account of the theory is given in Sommerfeld's Three 
lectures on Atomic Physics (Methuen, 1926). For its application to parti- 
cular elements see Grimm and Sommerfeld, Z.f. Phys. 1926, 86, 86 ; Som- 
mer, ibid. 37, 1 ; Laporte, J. Opt. Soc. Amer. 1926, 18, 1. McLennan, 
McLay, and H. G. Smith (Proc. Roy. Soc. 1926, 112, 76) give a complete list, 
based on the work of Heisenberg and Hund ; this agrees with the Table in 
nearly every case : but for each of the elements Re, Os, Ir, Pt, for which 
the spectra have not been fully worked out, they also suggest alternative 
formulae. For each of the last three elements (Th, Pa, U) they give two 
alternative formulae, neither of which is that in the Table : in the first of 
these it is supposed that the expansion of the fifth quantum group of 18 
may have begun, which would make these elements analogous to the rare 
earths, a view which their chemical behaviour does not seem to support 
f 6]ws S ^Z?? SUggestions of M <**^ McLay, and Grayson are as 
1 ts) Saturn groups are completely filled in all these 


^21 ^22 

5 32 5 33 

5 43 5 44 


^21 022 

6 32 6 33 

7 n 

75 Re 



2 4 



76 Os 



2 4 



77 Ir 



2 4 



78 Pt 



2 4 






2 4 

4 6 

90 Th 
91 Pa 
92 U 



2 4 
2 4 
2 4 
2 -4 
2 4 
2 4 


4 6 
4 6 
4 6 
4 6 
4 6 
4 6 

- . 



2 4 
2 4 
2 4 
2 4 
2 4 
2 4 





Detailed Structures of Atoms 47 

in doubt. But a comparison of this with earlier lists, such for 
*~ example, as that given by Coster in 1928, 1 shows that the deve- 
lopment of the theory has not seriously affected the essential 
conclusions, except in the distribution of the electrons of a group 
among the subgroups. Where the structure of an element is still 
in doubt, this is usually because the energies of the two alterna- 
tive orbits do not greatly differ, and hence the doubt is of less 
importance in interpreting the chemical behaviour of the element, 
which depends on the energy of these orbits. It must of course 
be remembered that the structure given for an element in the 
table is that of a ' normal ' atom, as Bohr calls it, that is, of an 
" isolated atom of the element, at a temperature low enough for 

it not to radiate energy, and to have its electrons in the most 
stable orbits possible. With some elements such ' normal ' atoms 
can scarcely be said to exist at all, except transiently in a dis- 
charge tube as for example with carbon, where the atoms remain 
combined up to temperatures at which some of the electrons 
must be far from their ' normal ' orbits. In such cases the finer 
details of the structure may be of less chemical interest ; but 
nevertheless a knowledge of the normal structure often gives us 
much information as to the chemical behaviour of the element, 
even when the normal atom is highly unstable. Thus the prob- 
able structure (on the spectroscopic evidence) of the normal 
palladium atom, which is that of a quasi-inert gas (2) (8) (18) (18), 
cannot apply to the element as we know it in the solid state : its 
metallic character shows that the fourth quantum group has 
been broken into, and that the solid, like all other metals, con- 
tains free electrons ; and the chemical evidence leads to the same 
conclusion. But the greater stability of the 18 group m this 
transition series as compared with the one before and the one 
after (which is what the structure of the normal palladium atom 
indicates), is clearly reflected in the chemical behaviour of the 
neighbouring elements, especially, as we have seen, in that of 
silver as compared with copper and gold. 

1 Naturwissenschaften, 11, 571. 


n = 1 




k, - ll 


2i2 2 


2 l2 a 

n do 



2i 2 a 

3 2 3 8 

4 A. 
o TXA 



2 He 


8 Li 



4 Be 























10 Ne 



2 4 

11 Na 



2 4 


12 Mg 



2 4 


18 Al 



2 4 



14 Si 



2 4 



15 P 



2 4 



16 S 



2 4 



17 Cl 



2 4 






2 4 


2 4 

19 K 



2 4 


2 4 


20 Ca 



2 4 


2 4 


21 Sc 



2 4 





22 Ti 



2 4 


2 4 






2 4 


2 4 



24 Cr 



2 4 


2 4 



25 Mn 



2 4 


2 4 



26 Fe 



2 4 


2 4 



27 Co 



2 4 


2 4 



28 Ni 



2 4 


2 4 



29 Cu 



2 4 


2 4 

4 6 


30 Zn 



2 4 


2 4 

4 6 


31 Ga 



2 4 


2 4 

4 6 



32 Ge 



2 4 


2 4 

4 6 



33 As 



2 4 


2 4 

4 6 



84 Se 



2 4 


2 4 

4 6 



35 Br 



2 4 


2 4 

4 6 



36 Kr 



2 4 


2 4 

4 6 


2 4 


n - 1 






kj - - 




2i2 2 

$2 3s 

4 8 4 4 


2i2 2 

3g 3 8 


87 Rb 





2 4 


88 Sr 





2 4 


39 Y 





2 4 



40 Zr 





2 4 



41 Nb 





2 4 



42 Mo 





2 4 



48 Ma 





2 4 



44 Ru 





2 4 



45 Rh 





2 4 



46 Pd 





2 4 

.4 6 


47 Ag 





2 4 


4 6 


48 Cd 





2 4 

4 6 


i _^_ 

49 In 





2 4 

4 6 



50 Sn 





2 4 

4 6 



51 Sb 





2 4 

4 6 



52 Te 





2 4 

4 6 








2 4 

4 6 



54 X 





2 4 

4 6 


2~ 4x 

55 Cs 





2 4 

4 6 


2 4 


56 Ba 





2 4 

4 6 


2 4 


57 La 





2 4 

4 6 


2 4 



58 Ce 





2 4 

4 6 



2 4 



59 Pr 





2 4 

4 6 



2 4 



60 Nd 





2 4 

4 6 



2 4 



61 n 





2 4 

4 6 



2 4 



62 Sm 





2 4 

4 6 



2 4 



68 Eu 





2 4 

4 6 



2 4 



64 Gd 





2 4 

4 6 



2 4 



65 Tb 





2 4 

4 6 



2 4 



66 Ds 





2 4 

4 6 



2 4 



67 Ho 





2 4 

4 6 



2 4 



68 Er 





2 4 

4 6 



2 4 



69 Tm 





2 4 

4 '6 



2 4 



70 Yb 





2 4 

4 6 



2 4 



71 Lu 





2 4 

4 6 



2 4 



72 Hf 





2 4 

4 6 

6 8 


2 4 





n = 1 





\ - 


,k, = - 





2i2 2 

3 2 3 8 


2i2 2 

3 2 3 8 


73 Ta 






2 4 



74 W 






2 4 



75 Re 






2 4 



76 Os 






2 4 



77 IT 






2 4 



78 Pt 






2 4 



79 An 






2 4 

4 6 


80 Hg 






2 4 

4 6 


V _^_ J 

81 Tl 






2 4 

4 6 



82 Pb 






2 4 

4 6 



83 Bi 






2 4 

4 6 



84 Po 






2 4 

4 6 









2 4 

4 6 



86 Em 






2 4 

4 6 









2 4 

4 6 


2 4 


88 Ha 






2 4 

4 6 


2 4 


89 Ac 






2 4 

4 6 


2 4 



90 Th 






2 4 

4 6 


2 4 



91 Pa 






2 4 

4 6 


2 4 



92 U 






2 4 

4 6 


2 4 




"TTALENCY is a general term used to describe the power which 
V atoms possess of combining with one another to form mole- 
cules. Our object is to explain this power m terms of atomic 
structure, that is, to discover the electronic mechanism by which 
atoms are held together, and to show how the variation of* 
valency from one atom to another is related to the arrangements 
of the electrons in these atoms. We must therefore first consider 
what we can learn of the nature of valency from the chemical 

The earliest serious theory of valency was that of Berzelius(1812), 
who assumed that the force between atoms was purely. electro- 
static, that the molecule of sodium chloride, for example, was 
held together by the attraction of a positive charge on the sodium 
and a negative charge on the chlorine. This theory, which was 
strongly supported by the phenomena of electrolysis, was over- 
thrown as a universal theory of valency about 1840 from its 
inability to account for certain facts of organic chemistry, 
especially the replacement of positive hydrogen by negative 
chlorine without any fundamental change m the properties of 
the molecule (Dumas, 1884). The rival theory, that of structural 
chemistry, made no assumptions as to the nature of the force 
between the atoms, but regarded it as essentially non-polar, that 
is, as not involving any opposite character in the two linked 
atoms. The enormous success of this theory in the sphere of the 
carbon compounds rather obscured the fact that the electrical 
theory of Berzelius still remained quite satisfactory if it was con- 
fined to the linkages between oppositely charged ions in a salt. 
In 1869 it was pointed out by Mendele'eff, in his original formula- 
tion of the Periodic Law, that the numerical value of the valency 
is closely related to the periodic groups, and normally changes 
by one unit when we pass from one group to the next. 

With the rise of the Arrhenius theory of electrolytic dissocia- 
tion in and after 1887 the views of Berzelius again came to the 
front, and it became clear that atomic linkages are of two kinds, 
one iomzable and presumably due to electrostatic attraction, and 
the other non-ionizable, and not explicable in this simple way ; 
but this distinction was not much regarded, mainly because the 

54 Electronic Mechanism of Valency 

Kossel 1 pointed out that the element next before an inert 
gas is always a strongly electronegative and univalent halogen, 
and that immediately following an equally strongly electro- 
positive and univalent alkali metal : that the element next 
before the halogen is negative and divalent, and that next follow- 
ing the alkali metal positive and divalent, and so on : and that 
these facts could be simply explained by supposing that the inert 
gas had a stable arrangement of electrons which the other ele- , 
ments strove to attain by acquiring or losing the necessary num- ** 
ber of electrons. For example, in the series 

S' Cl A K Ca ^ 

16 17 18 19 20 

eighteen electrons must be capable of a stable arrangement (since 
argon, m which this number occurs, is inactive), and this arrange- * 
ment chlorine could assume by taking up one, and sulphur by 
taking up two electrons : while potassium could do the same 
by losing one and calcium by losing two. This would give the 
stable ions (all with eighteen electrons) S", Cl~, K + , Ca ++ , which 
by combination would yield the neutral salts K 2 S, KC1, CaCl 2 , 
&c., in which the electronegative part had gained the necessary 
electrons at the expense of the electropositive part, the ions in 
the salt being held together by the electrostatic forces so pro- 
duced. On this theory it appears that the valency of an atom is 
the number of electrons it must gam (if electronegative) or lose 
(if electropositive) in order to haye a total number capable of 
r forming a stable arrangement. 

Kossel points out that the existence of ions with these charges 
can be proved by physico-chemical methods for all elements one 
or two places from an inert gas, and claims that similar ions can 
be assumed by analogy to exist with more remote elements (as 
in NH 3 and PH 3 ), though he admits that with them the tendency 
to ionize is less. These simple relations break down when we 
come to the elements near the middle of the long periods (transi- 
tion elements in the wider sense), but they still hold for the 
neighbours of the inert gases in every period. He illustrates his 
theory by a diagram in which the actual number of electrons in 
the ion is plotted against the atomic number, and shows that if 
we interpret valency in his way, the actual number tends to be 
that of the nearest inert gas. 

This theory is based upon atomic number, but it does not 

1 Ann. d. Phys. 1916, 49, 229. 

Kossel : Polar Links 55 

involve the acceptance of any particular atomic model : it only 
assumes that some of the electrons 1 are firmly held and unaffected 
by external influences, while there are others loosely bound, 
which are active in chemical combination, as they are in pro- 
ducing the optical spectra. (It will be noticed that Drude had 
very nearly arrived at this view twelve years earlier, though he 
could not assign specific numbers of electrons to the atoms.) 

Kossel's theory explains the connexion -between the valency 
pf an element and its position in relation to the inert gases. It 
accounts for the peculiar characteristic of the chemical link that 
it satisfies one unit of combining power of each of the atoms 
concerned, and it is in complete agreement with the results of 
the electrolytic theory. Further support has since been given to 
it by the results of spectroscopy and of the X-ray examination 
of crystals. On all these grounds its truth cannot be doubted, 
so far as a particular class of compounds is concerned. It is ihfc 
essence of the theory that the two linked atoms should be dis- 
similar in character, one tending to lose and the other to gain 

But there are many molecules in which it is difficult or im- 
possible to say which is the positive and which the negative atom, 
such as sulphur dioxide, carbon dioxide, or still more strikingly 
the diatomic elementary gases like hydrogen, oxygen, nitrogen, 
and chlorine. There is no reason to think that in hydrogen, for 
example, either atom has lost an electron to the other. Nor do 
such compounds or elements ionize in solution. The existence 
of two kinds of linkage, ionized and non-ionized, had been 
apparent from the time of the overthrow of the Berzelius theory, 
and had been made still more evident by the work of Arrhenius 
and van't Hoff ; and it was clear that Kossel's theory of electro- 
nic transference, while it was quite satisfactory as an explanation 
of the ionized link between dissimilar atoms, was entirely in- 
capable of accounting for non-ionized links between similar 
atoms : this was indeed recognized by Kossel himself. The 
problem is not merely to discover a mechanism by which atoms 
can be united without the transference of electrons, but also to 
explain why the numerical value of the valency is the same, at l 
any rate in simple instances, for both kinds of linkage. Thus 
hydrogen and chlorine are univalent, and oxygen is divalent, 
whether they are combined with carbon, or with metals, or with 
one another, and whether the resulting molecules are ionized 
or not. 

56 Electronic Mechanism of Valency 

The solution was given in the same year (1916) by G. N. 
Lewis. 1 He assumed, like Kossel, that the cause of chemical 
combination is the tendency of the electrons to redistribute them- 
selves among the atoms so as to form more stable arrangements 
such as occur in the inert gases ; but he made an advance of 
fundamental importance by suggesting that it was possible for 
an electron to be shared between two atoms so that in some 
way it could count towards the stability of both. How this 
sharing was effected he did not discuss : in fact with his static 
model (the ' cubic atom ') this question did not arise, since the 
existence of such an atom could not" in any case be explained 
without the assumption of unknown forces. With a dynamic 
model such as we now accept, the question becomes of great 
importance, though it can only be very imperfectly answered in 
the present state of our knowledge. For our immediate purpose, 
however, it need not be discussed : if we assume that such shar- 
ing is in some way possible, so that each electQpn enters into the 
constitution of both atoms, we can at once account for the 
valency of atoms in their non-ionized compounds. Chlorine, 
for example, has one electron less than the stable number 
of 18. Hence, as we^have seen, it readily takes up an electron 
from an atom that readily loses one, such as sodium, to form 
a chlorine ion with a negative charge. But it can also com- 
plete its number of electrons by sharing one belonging, say, 
to another chlorine atom ; and if at the same time the second 
chlorine atom shares another electron belonging originally to 
the first, then each is satisfied. The various states of the atom 
are shown below, the dots and crosses representing valency 
electrons, without any assumption as to their positions in space : 
in the atomic symbols beneath, the shared electrons are under- 
lined : 

: ci : ci ; : ci ; ci ; 

* * "" *"xx 

CI = (2) (8) (7) [CI]- = (2) (8) (8) -CI = (2) (8) (6, 2) 

The Kossel method of linkage is primarily confined to com- 
pounds between elements of opposite character : it enables an 
atom that has too many electrons for stability to give up the 
excess to atoms that have too few. The Lewis method, on the 
other hand, enables a smaller number of electrons to*7To the work 
of a larger : it is essentially a linkage for atoms each of which is 
1 J. Amer. Ckem, Soc. 1916, 38, 762. 

Lewis : Non-polar Links 57 

a few electrons short of a stable number, i.e. for electronegative j 
atoms. This entirely agrees with experience. Non-ionized com- 
pounds are far commoner among electronegative elements : j 
they are comparatively rare among the metals. To distinguish 
these two forms of linkage Langmuir suggested the very con- 
venient terms ' covalency ' and ' electrovalency ', which have 
been generally adopted. 

Another conclusion of fundamental importance is that the 
numerical value of the valency is the same on both theories. The 
electrovalency of Kossel is equal for a negative element to the 
number of electrons that it needs to make up a stable number. 
Since on the Lewis theory it gains an % electron for each covalency 
that it forms, the number of covalencies must be equal to this 
defect, and so to the electrovalency. For a positive element, the 
electrovalency is equal to the number of electrons in excesfe of 
a stable number. On the Lewis theory the atom in forming a 
covalency must not only share an electron belonging to the other 
atom, but also give to the other atom a share in one of its own 
electrons, and therefore the number of such links which it can 
form cannot exceed the number of electrons which it has to offer, 
so that here also the covalency and the electrovalency are -. 

numerically equal. Thus we can see why chlorine is univalent \s 
in methyl chloride as well as m sodium chloride, and zinc divalent 
in zinc methide as well as in zinc sulphate. 

The necessity of two shared electrons to every covalent link^/' 
is an essential part of the Lewis theory ; and as this assumption 
has been questioned, its justification must be considered. The 
most fundamental conclusion of the chemical study of valency, 
quite apart from any question as to its mechanism, is that every 
link, whether ionized or not, satisfies one unit of combining 
power of each of the two atoms which it unites. The single link 
between the sodium and the chlorine in sodium chloride satisfies 
both the single valency of the sodium and that of the chlorine : 
when carbon with four valencies unites with four hydrogen atoms 
which have one each, four links are formed, each of which satis- 
fies one unit for the hydrogen and one for the carbon. The pro-, 
cess is analogous to the linking of two hooks, one for each atom,; 
and not to the hanging of a series of hooks from a ring. Any 
proposed mechanism of valency must take account of this fact. 
The Kossel theory does so, because on that theory the electron 
lost by one atom must be taken up by the other, since the whole 
molecule is electrically neutral. The Lewis theory only does so 

58 Electronic Mechanism of Valency 

if with Lewis we make the additional assumption that ever} 
covalency requires two electrons to be shared between the twc 
atoms. For example, fluorine is umvalent : its structure is (2) (7) 
and so is one electron short of the stable number of neon, (2) (8) 
It can make up this defect in combination with sodium, bj 
taking the loose electron from a sodium atom. It can combine 
with carbon (2) (4), which has four valency electrons, and alsc 
is four short of the neon number, by four fluorine atoms eacl- 
sharing one of the valency electrons of the carbon. This gives 
each fluorine atom the extra electron which it needs. But we 
know that in this combination the carbon also is satisfied, sc 
that it must have acquired four electrons in addition to the foui 
which it had originally, and which it can still use although it has 
shared them with the fluorines. This means that every time it 
makes a link by sharing one of its own electrons with a fluorine 
atom, it also shares one of the electrons belonging to the fluorine 
a link is formed with each fluorine, consisting of a shared 
electron from the carbon and one from the fluorine, so that the 
carbon, as well as the four fluorines, has its valency electrons 
made up to eight, the compound being written 

:'*': F 

: F : c : F : or F c F 

We shall see later (p. 102) that there is evidence showing that 
in a small number of unstable compounds hydrogen can be 
attached to one of the lighter atoms by a covalent link formed 
of a single shared electron : but such links are exceptional. In 
.all ordinary compounds two electrons are required ; indeed, i1 
/it were not so, one atom might satisfy the affinity of anothei 

', ( without satisfying its own, or limiting its power of combination 

f with further atoms. 

Thus the theories of _Kossel and of Lewis provide an electronic 
mechanism for the two kincls of linkage, polar and non-polar, 
which the chemical evidence requires. So far they make little 
change m the accepted structural formulae. We distinguish the 
ionized links by Werner's device of the square brackets en- 
closing the non-ionizably attached atoms of a polyatomic ion, 
and with the non-ionizable links themselves we merely substitute 
two dots for a line. We then find (at any rate for the normal 

Lewis : Non-polar Links 59 

compounds of the lighter elements) that hydrogen, unless it is 
ionized, always has two electrons, and the ^otEef atoms are each 
provided with eight electrons, shared or unshared. But in the 
same paper Lewis makes a further suggestion, which has subse- 
quently been shown to explain the co-ordination compounds of 
Werner. He says : 1 ' While the two dots of our formulae ' 
(indicating two shared electrons) ' correspond to the line which 
has been used to represent the smgle bond, we are led through 
their use to certain formulae of great significance which I pre- 
sume would not occur to any one using the ordinary symbols. 
Thus it has been generally assumed that what is known as a 
bivalent element must be tied by two bonds to another element 
or elements, or remain with an " unsaturated valence ". On the 
other hand we may now write formulae in which an atom of 
oxygen is tied by only one pair of electrons to another atom, and 
yet have every element in the compound completely saturated. 
To illustrate this important point we may write the formulae of 
perchlorate, sulphate, orthophosphate, and orthosilicate ions, in 
which each atom has a complete shell of eight electrons. Thus 





represents all of these ions. If X is chlorine, the ion has one 
negative charge : if sulphur, it has two negative charges, and 
so on.' 

The full significance of this conception will be apparent later, 
but the fundamental idea is simple. A divalent atom like 
oxygen needs two more valency electrons. It can gam these by 
forming two covalent links, that is, by sharing two electrons 
belonging to another atom or atoms, while at the same time the 
other atom or atoms share two belonging to the oxygen 

R * O ; R = R-O-R . 

This is the usual divalent oxygen of structural chemistry. The 
new mode of combination which Lewis suggests is that the oxy- 
gen only forms a single covalency only shares two electrons 

1 Loc. cit. p. 778. 

60 Electronic Mechanism of Valency 

with the other atom but that both of these electrons come froi 
the other atom 

R; + o : > R; o : 

This constitutes only a single link, but it increases the valenc 
electrons of the oxygen by two, and therefore the oxygen be 
comes saturated. In other words, he suggests that the two share 
electrons which, constitute a covalency can arise in two ways 
(1) as they normally do, by each of the atoms concerned conta 
1 buting one of them ; or (2) by one of the atoms contributing bott 
The application of this idea to the oxy-acids of the type H D XO 
is clear. The eight shared electrons in the ion 

: b : 
: o xX'o : 

XX ' 

: o : 

are all needed to make up the valency groups of the four oxygen, 
from six to eight ; hence they are not derived from the oxygens 
but either from the central atom X or from outside, and ever] 
electron coming from outside must give the molecule a negativ< 
charge. If X is chlorine, with seven electrons to start with, i 
will need one more, giving the univalent ion [C10 4 ]' : if it i; 
sulphur, with six, it will need two more, giving [SO 4 ]" : in tht 
same way phosphorus will need three and silicon four, so thai 
we arrive at the familiar formulae HC1O 4 , H 2 S0 4 , H 3 PO 4 
H 4 Si0 4 . 

This new type of covalency needs a name and a symbol. 11 
may be called a co-ordinate link, since it affords, as will be showi 
later, an explanation of the co-ordination compounds of Werner . 
and it may be expressed in formulae by an arrow (in place oJ 
a line) pointing away from the atom which contributes the twc 
electrons : 1 

A' + X B > A ; B = A-B 

Normal Covalency. 


A! + B > A : B = A^B 

Co-ordinate Covalency. 

1 This is the ' semi-polar ' link of Lowry and others, which is also written 
A-B or AzB. See further Chapter VII. 


Relation to Structural Theory ' 61 

In forming co-ordinate links an atom will obviously not be 
subject to the same limitations (according to its periodic group) 
as in forming normal links. Sulphur, for example, can as a rule 
only form two normal covalencies, as in (CH 3 ) 2 S, because these 
give it the full valency group of eight. Of these eight, two pairs 
are shared with the two carbon atoms, while the other four are 
not shared, and form what the Americans call ' lone pairs '. 
But though the sulphur atom in (CH 8 ) 2 S is in this sense satu- 
rated, it can form two more covalencies of the second type, by 
sharing these Jone pairs with atoms, for example, of oxygen, 
wTHch'need two electrons to make up their full complement. 
Thus the possibility of co-ordination enables the sulphur atom 
to increase its covalency from two to four. 

: o : 
H 3 c ; : CH S H 3 c ; : CH, H 3 c ; : CIL 

3 * x x 3 3 x x 3 3 x x * 

: o : : o : 



H 3 C-S-CH 3 H 3 C-S-CH 3 H 3 C-S-CH 3 

O O 

We thus arrive at a mechanism for the three types of linkage 
which as we have seen (p. 52) the chemical evidence shows to 

(1) Polar or ionized linkages : due to the transference of 
electrons from one atom to another (electrovalency). 

(2) Non-polar, non-ionizable (covalent) linkages : due to the) 
sharing of electrons, two to each link, between the atoms. These 
can arise in two ways : 

(a) One electron contributed by each atom : normal covalencies :l 

limited in number (like electrovalencies) by the periodic! 
group of the atom. 

(b) Both electrons contributed by the same atom : co-ordinate 

covalencies ; when these are formed the numerical value! 

of the covalency is no longer dependent on the periodic i 

group to which the atom belongs. 

So much for the electronic mechanism of the linkages them- 
selves. The reason for their formation is that they produce more 
stable groups of electrons than the isolated atoms possess, groups 
such as are found m the inert gases. Now with the exception of 

62 Electronic Mechanism of Valency 

helium, which has a single group of two electrons, all the inert 
gases have been shown to have an outer group of eight. It was 
therefore originally assumed that the redistribution of electrons 
in chemical combination led to the production of a valency group 
of eight with all atoms except the immediate neighbours of 
helium (hydrogen, lithium, beryllium), where the number was 
two. This was the foundation of the octet theory of Lewis, first 
published in 1916 (loc. cit.) and subsequently developed by him- 
self, Langmuir, and others. The progress of physics has shown 
that the static atom must be given up, and with it the spatial 
relations involved in the cubic octet. But it is still true that in 
a very Jarge_ number_pf compounds the stability of atoms is 
determined by their having a group of eight valency electrons : 
so that the octet, regarded simply as a number of electrons, 
retains its importance for many purposes. If we assume that it 
represents the maximum number possible in a valency group, 
and at the same time accept Lewis's theory that two electrons 
are required to form a covalency, we must conclude that the 
largest number of covalent links that any atom can form is four. 
The compounds of the elements of the first short period (down 
to fluorine) support this view. But in the second short period 
(Na 11 to Cl 17) we meet with a serious difficulty in sulphur hexa- 
fluoride SF 6 . This is a gas (boiling below 50) of quite extra- 
ordinary stability. It can be passed through water or even hot 
potash solution without change : it is not acted on by sodium 
below a red heat. These properties make it clear that it is not 
a salt, but a covalent compound like carbon tetrafluoride. Since 
we never find two fluorine atoms joined together (except in 
elementary fluorine) all the six fluorine atoms must be attached 
by covalent links to the sulphur. If each link consists of two 
shared electrons, the whole valency group must contain twelve. 
The sulphur atom is obviously suited to form such a compound, 
since it has six valency electrons to olfer for the six links. The 
links cannot be formed of single electrons, because such links 
must be (and are always found to be) very weak, whereas the 
stability of sulphur hexafluoride is abnormally great. A further 
examination of the compounds of the heavier elements shows 
that this is no isolated case, but is one of many : for example, 
in addition to the numerous other hexafluorides, all Werner's 
optically active compounds of chromium, cobalt, and other metals 
belong to this category. 
We must therefore conclude (as Lewis himself subsequently 

Limits of Valency Groups 63 

did) that the valency group is not_limited to eight, but can with 
some atoms rise_to twelve. Even this is not the maximum, for 
we find a volatile octofluoride of osmium OsF fi in which we must 
assume a valency group of sixteen electrons. 

Before we go on to discuss in more detail the criteria of the 
different forms of linkage and the conditions of their stability, it 
will be useful to consider the application of these fundamental 
ideas to some of the simpler and more familiar types of com- 
pound, taken mainly from the first short period of Mendele"eff. 

Periodic group 1234667 

Element (H 1) (He 2) 

Li Be B C N O F Ne 

Atomic number 3456780 10 

Valency electrons 1234567 (8) 

All these elements from lithium onwards have an inner (1 -quan- 
tum) group of two electrons, and hence their number of valency 
electrons is two less than the atomic number, and is of course 
equal to the group number in the periodic table. It is convenient 
to distinguish those electronic groups which are not affected in 
chemical combination as the core of the atom, in contrast to the 
outer group of valency electrons which is modified in combina- 
tion : thus in all these elements after hydrogen there is a core of 
two. The ' stable arrangements ' to which all these elements 
tend in their compounds are those of the inert gases helium (2) 
and neon (2) (8). 

On these principles we can answer the much disputed question 
whether hydrogen should be regarded as belonging to the alkali 
metals or to the halogens : it clearly has properties in common 
with each class. The alkali metals are typical univalent metals ; 
they have one electron more than an inert gas, and this electron 
is therefore easily lost. Hydrogen, consisting of a nucleus of 
one proton with a single attendant electron, also loses this 
electron easily, leaving the proton that is, the hydrogen ion 
behind. In this respect it is like an alkali metal. The halogens, 
on the other hand, are typical univalent electronegative ele- 
ments, having one electron less than an inert gas, and so very 
ready to take one up, either by transference to give a univalent 
anion, or by sharing, as in fluorine gas or methyl fluoride. Hydro- 
gen, while it has one electron more than a proton, has one less 
than helium, and so it readily takes one up, just as a halogen 
does. This it usually does by sharing, as in the hydrogen mole- 
cule H;H, or in a hydrocarbon. It can also, however, in 

64 Electronic Mechanism of Valency 

combination with highly electropositive metals, form a negative 
ion ['H*]~; this behaviour was predicted by Lewis in 1916, 
and subsequently verified experimentally in the cases of lithium 
and calcium hydrides Li[H] and Ca[H] 8 . 

The elements from lithium (8) to fluorine (9) might either lose 
electrons so as to revert to the helium structure, or gain them 
so as to attain that of neon. As we should expect, the_earlier 
elements tend to lose, and the later to gam electrons. Thus we 
have the simple ions Li + and Be ++ with two electrons each, and 
O~~ and F~ with ten. The formulae of their compounds are 
easily written (square brackets [ ] always enclose an ion). 

The intermediate elements boron, carbon, and nitrogen do not 
form simple ions at all, but only covalent compounds, and as this 
necessarily involves an increase in the number of electrons, they 
never revert to _ the helium structure, but always progress Tx> 
wards^ that^ of neon : they strive to complete their octets. For 
tfiis purpose carbon (boron will be dealt with later) needs four 
and nitrogen three more electrons. In consequence carbon com- 
bines with four and nitrogen with three hydrogen atoms, giving 

H H 

X X 

H ; C : H and H ? N ; H 



in both of which the octets are complete. When we come to 
hydrogen and oxygen, there is a difficulty : water may equally 
well, so far as formulae go, be written 

H:O;H, [H];O:H, or 

(in the ordinary symbols H-O-H, [HJO-H, or [H]0[H]), accord- 
ing as we regard the molecule as ionized (electrovalent) or not 
(covalent). The question can only be decided by considering 
the properties of water, which will be done later: but it is probable 
that (apart from polymers) water is a mixture consisting mainly 
of non-ionized but to a small extent of ionized molecules. 

Most of the simpler organic compounds, in which the linkages 
are nearly always covalent, can be formulated quite easily on these 
principles. In such molecules as CH 3 OH, H 2 CO, CH 3 CO OC 2 H 6 , 

Application to Lighter Elements 65 

CH 3 NH 2 it is only necessary to substitute two dots for every 
line in the full structural formulae': a single bond corresponds to 
two and a double bond to four shared electrons. It is scarcely 
necessary to say that such complete electronic formulae need 
not be adopted for ordinary use. Just as the student only 
writes the usual structural formulae in full until he understands 
them, and substitutes contractions like C 2 H 6 or C0 2 H as soon 
as he realizes what these contractions mean, so he need only use 
the electronic formulae until he is familiar with them ; he can 
revert to the simpler structural symbols as soon as he is able 
to transform them into their electronic equivalents when re- 
quired, or when any difficulty arises. Almost the only one of 
the commoner organic groups whose conventional formula 
is modified by these new ideas is the nitrp-group. On the 
classical theory this could be written in~either of two ways : 

(1) R-N<g? or (2) R-N<9 . The conception of the co-ordi- 

nate link introduces a new possibility, (3) R N<^u, the 

nitrogen completing its octet at the mtroso stage R N=O or 


R?N;O; , and in the formation of the nitro-compound sharing 


its remaining ' lone pair ' of electrons with a second oxygen 
atom. There is strong evidence that this third structure is 
correct. Nitrogen can be shown to be incapable of forming more 
than four covalent links, so that formula (1) is excluded : (2) is 
improbable owing to the great strain involved m a 8 -ring (recent 
work has shown that 3-rings containing a nitrogen atom are much 
less frequent m organic chemistry than was previously supposed) : 
and finally the mtro-compounds show all the properties charac- 
teristic of molecules with co-ordinate links x (see Chapter VII). 
The relations between tri- and qumquevalent nitrogen are 
easily explained in the light of the electronic theory. Nitrogen 
has five valency electrons, and so can complete its octet by 
taking up three hydrogen atoms. This octet is made up of six 
shared electrons and two unshared (a lone pair). If a fourth 
(neutral) hydrogen atom were taken up, this would introduce 
another electron, and the valency group would consist of nine, 
as it does in sodium (2) (8) (1). Hence (neutral) NH 4 behaves 
like a univalent metal : the valency group is unstable : it loses 

1 This structure has recently been confirmed by Sugden's measurements 
of the parachor (see p. 127). 

3k K 

66 Electronic Mechanism of Valency 

one electron readily if there is anything present that can receive 
it, and forms the stable ammonium ion 



H ; N r H 


The core of the atom does not alter, and in that sense there is no 
real change of valency. This explains why it is found that one of 
the five valencies of quinquevalent nitrogen must always be tin 
electrovalency : the formation of an electrovalency the expul- 
sion of an electron is the condition of the nitrogen becoming 
4-covalent. A nitrogen atom which has lost one of its electrons 
has four left, and so behaves like carbon. The resemblance 
extends to the positions of the four attached groups in space. 
In carbon they are as we know arranged at the points of a tetra- 
hedron, giving optical activity when they are all different ; so 
also with nitrogen the four covalently attached groups of the 
ammonium ion have been proved to be at the points of a tetra- 
hedron (Mills and Warren, 1925), and the optical activity is 
determined by them alone : the fifth group, the anion, is not 
attached to the ammonium ion m any fixed position, but merely 
attracted to it as a whole. 

This principle, that an atom which has lost an elccfron re- 
sembles the preceding element, is (like the radioactive and the 
spectroscopic displacement laws) 1 a direct result of the theory 
of atomic number, and is of very wide application. Oxygen, 
having six valency electrons, can take up two hydrogen atoms 
or two methyl groups, and so complete its octet, which then 
consists of four shared and four unshared electrons : it is a 
divalent element. But if it loses an electron (and so acquires 
a positive charge) it becomes, like neutral nitrogen, a trivalent 
element ; for it then has five electrons, and has room for three 

more. Thus the oxygen in methyl ether H 3 C ; O : CH 3 is 
saturated in the same sense as the nitrogen in ammonia. But 
if it expels an electron it can take up a hydrogen atom, becoming 


1 pp. 7 and 87. 


Application to Lighter Elements 67 

This of course can only be isolated in electro-combination with 
an anion such as [Cl]~, and thus we have an explanation of 
the existence of the compound methyl ether hydrochloride 
(CH 8 )OHC1, and of the oxonium compounds generally. The 
same change occurs with the halogens, though less easily and 
not with the lighter members, but certainly with iodine. The 

iodine in phenyl iodide C 6 H 5 1 I \ is saturated, having made 

its seven electrons up to eight. By losing an electron it acquires a 
positive charge and at the same time becomes divalent like 

neutral oxygen ; it can thus form the ion [C 6 H B * I ' x C 6 H 6 ] + in 

the well-known iodonium salts, such as [(C 6 H 5 ) 2 I]I. 

The elements of the fifth, sixth, and seventh groups nitrogen, 
oxygen, and fluorine in the first period are thus limited in their 
valency by the number of electrons for which they have room. 
Nitrogen can only take up three, oxygen two, and fluorine one, 
in order to complete the octet ; and as every univalent atom or 
group brings an electron with it, their valencies in the neutral 
state are limited (apart from co-ordination) to three, two, and 
one, respectively. By expelling an electron and becoming cations 
they increase their valency by one. 

With the elements preceding carbon (so far as they form co- 
valencies) there is the opposite difficulty. Boron, for example, 
has three valency electrons. It has room for five more ; but it 
cannot take up five univalent groups, because it has not got five 
electrons to offer for the five links, but only three. Hence it 
can only take up three univalent groups, as in the fluoride BF 3 
or the methide B(CH 3 ) 3 (the structure of B 2 H 6 will be discussed 
later it is almost certainly one of the rare instances of hydrogen 
attached by a single shared electron). In BF 3 the boron has lent 
one electron to each halogen atom, and borrowed one from each : 

. F * B ; F ; 

so that the fluorines have completed their octets, while the boron 
has to be satisfied with six shared electrons, two for each link. 
This is an unstable condition, and atoms with incomplete octets 
are always ready to complete them. Now if the boron took up 
another electron, it would be able to combine with a fourth 
group : it would have four valency electrons like carbon, and 


Electronic Mechanism of Valency 

would like carbon be quadrivalent, but it would have a negative 
charge. It does this : it takes up an electron and a fourth 
fluorine atom, giving the stable anion [BFJ~, corresponding to 
[NHJ+, in which the octets of all the atoms are complete. 

: F : 
: F ; B : F : 


: F : 

In this way we get a neutral and stable salt K[BF 4 ], commonly 
described as a double salt, although no one would call the com- 
ponent BF 3 a salt. 

A similar explanation applies to a more familiar series of 
' double salts ', the silicofluorides. Sulphur, as we have seen, 
forms a very stable compound SF 6 , in which it must have a 
valency group of twelve, lending one of its six electrons to each 
fluorine atom. Silicon has only four valency electrons, and so 
forms SiF 4 . But if the silicon can gain two more electrons, giving 
it six like sulphur, it can combine with six fluorine atoms to 
form SiF 6 , which of course has two negative charges. Thus in 
presence of a fluoride silicon tetrafluonde forms the stable anion 
[SiF 8 ]~ ~ of the silicofluorides M 2 [SiF 6 ]. Aluminium, with three 
electrons to start with, can do the same thing if it gains three 
more : and so we get cryolite Na 3 [AlF 6 ]. 

This process, in which there is a change of valency accom- 
panied by a gain or loss of electrons, deserves a rather more 
careful consideration. The most familiar example, the conver- 
sion of ammonia into the ammonium ion, has been described as 
consisting in the taking up by the ammonia of a neutral hydrogen 
atom, followed (or accompanied) by the expulsion of an electron. 
This is quite correct, but the same process may be described 
with equal truth in another way. The actual condition of the 
change is, as we all know, that the ammonia should come in 
contact with an acid, that is, with hydrogen ion. Presumably 
therefore the reaction should be written as taking place between 
an ammonia molecule and a hydrogen ion : 




H ; N ; H 



Co-ordinate Links 69 

In that case we ought to say that the nitrogen of the ammonia 
shares its ' lone pair ' with the hydrogen ion, or that this hydro- 
gen is attached to the nitrogen by a co-ordinate link. This is not 
only as true an account of the structure of the ammonium ion as 
that previously given, but it is really the same account in differ- 
ent language. On either view it is agreed that in the ammonium 
ion every hydrogen atom shares two electrons with the nitrogen : 
that in this way every hydrogen atom acquires the two electrons 
necessary to its stability, and the nitrogen atom its octet : and 
finally that the whole molecule has one positive charge ; which 
is explained on the first view by saying that since there are only 
eight valency electrons left in the octet, while one neutral nitro- 
gen atom and four neutral hydrogen atoms originally had nine 
between them, one electron has been expelled ; and on the 
second view by the fact that a molecule made up of a neutral 
ammonia and a positive hydrogen ion must have a positive 
charge. It is not to be supposed that there is any difference 
between the linkage of the ' co-ordinated ' hydrogen to the 
nitrogen and those of the other three hydrogen atoms : each 
link consists of two shared electrons. In precisely the same way 
the formation of [BF 4 ]~ or of [SiF 6 ]~ ~ may be described as due 
to the co-ordination of one fluorine ion to the boron, or two to 
the silicon : 

F:B + TiF:] 

. . x . L J 

: F : 

: F 
F : B 

.1 x> 

: F 


Some confusion may arise from the statement that the co- 
ordinate link in such molecules does not differ from an ordinary 
covalency, when we have already adopted a special symbol to 
distinguish co-ordinate from normal covalencies : but the con- 
tradiction is only apparent. The co-ordinate link when it is estab- 
lished has the same mechanism as an ordinary covalency: the 
difference is in the way it is established. A normal covalency A B 
between two atoms increases the number of electrons in each by 
one : a co-ordinate valency A->B increases the valency group 
of one atom (B) by two, while it leaves that of the other (A) un- 
changed. The symbol N-H means that each atom shares an 
electron previously belonging to the other. If we wish to express 
the fact that the fourth hydrogen atom in ammonium is a 

70 Electronic Mechanism of Valency 

co-ordinated hydrogen ion we should not write it N-H, since 
this would mean that the nitrogen shared its lone pair with a 
hydrogen atom (that is of course a neutral atom), which there- 
fore would have three electrons one which it had to start with, 
and two gained from the nitrogen. If it is to be treated as a 
co-ordination compound, the components are not ammonia and 
a hydrogen atom, but ammonia and a hydrogen ion, and the 
group would therefore have to be written N->[H] + , which 
indicates that the nitrogen has shared its lone pair with a hydro- 
gen ion, and that this hydrogen now has two electrons none to 
start with, and two gained from the nitrogen. But there is no 
point in using this complicated symbol when the outcome of the 
J whole change is to link the fourth hydrogen to the nitrogen in 
I the same way as the other three ; for they also are each joined 
by two shared electrons, and though we may say that here one 
of the two comes from the nitrogen and the other from the 
hydrogen, one electron does not in itself differ from another, and 
the only use in distinguishing their origin is to enable us to count 
them up correctly. In the same way [BFJ~ might be written 
F B-<-[F] , but this for the same reason is an unnecessary 


elaboration. Such formulae would indeed have a meaning if we 
wished to imply that the electric charge which the ion as a whole 
must possess resided in one particular atom. But there is no 
reason to think that it does so. The charge will be divided 
among the atoms of the ion in proportions depending on the time 
spent by the shared electrons in different parts of their orbits, 
about which we know little or nothing, except that the distribu- 
tion will be uniquely determined by the number and nature of 
the atoms, and that the share of each of the hydrogen (or 
fluorine) atoms will be the same. 

I have perhaps discussed this question at unnecessary length, 
but I have found that it is one which is not unfrequently mis- 

In these particular instances of [NH 4 ] + , [BF 4 ]~, and [SiFJ", 
if they are regarded as co-ordination compounds, one of the 
components is an ion, and so the products are idns also. This 
however need not be so : two neutral components may form 
a co-ordinate link if one of them can supply a ' lone pah- ' and 
the other can take it up. That an oxygen atom can act in this 

Co-ordinate Links 71 

way was recognized, as we have seen, by Lewis. Ammonia 
might form such a compound with oxygen 

H .. ? 

H:'N:O; or H-N-+O; 

X X X I 

H H 

and though this compound is not known (unless it be as a tauto- 
meric form of hydroxylamine), the corresponding oxides of the 
tertiary amines, such as trimethylamme oxide (CH 3 ) 3 NO, are// 
well established. They are commonly written with a double link 
between the nitrogen and the oxygen, but since we know that 
nitrogen cannot form more than four covalent links, they should 
obviously be formulated R 3 N-0. It is interesting that methyl-, ' 
ethyl-aniline oxide, in which all the three hydrocarbon radicals*^ \ 
are different, has been shown to be optically active. ' 

With a link of this kind it is evident that the oxygen, which 
began as a neutral atom with a nuclear charge of + 8, balanced by 
two K (1 -quantum) electrons and six valency electrons, has now 
acquired in addition a share in two more electrons, borrowed 
from the nitrogen. This must give it something of a negative 
charge, the nitrogen having a corresponding positive charge ; ^ 
and if we assumed that the two electrons are shared equally 
between the two atoms, we should conclude that the oxygen has 
one unit of negative and the nitrogen one unit of positive charge. 

+ - + - 

For this reason Lowry writes the link A B, as in R 3 N O, 

and calls it a semi-polar link : it is regarded as made up of one 
polar and one non-polar link (one electrovalency and one co- 
valency). We know so little, however, about the mechanism of 
the sharing of electrons, or about the distribution of the charge 
among the atoms concerned, that it is perhaps safer to make no 
assumptions in the matter. We must recognize that the nitrogen 
in an amine oxide is essentially in the same state as in an 
ammonium ion, having eight shared electrons forming four 
covalent links ; but it is better to adopt a symbol which does not 
prejudge the question of the distribution of the electrical charge, 
so long as it is realized that some degree of electrical polarity, 
in the sense discussed above, is produced by co-ordination. 

Boron affords another example of a link of this kind. The 
boron atom in boron trimethide has, as we have seen, only six 
(shared) valency electrons. It can therefore take up two more, 
and so combines with ammonia to form (CH 3 ) 3 B--NH 3 , a stable 

72 Electronic Mechanism of Valency 

compound melting at 56 and boiling at 110. The occurrence 
of links of this type in the oxy-acids H 3 PO 4 , H 2 S0 4 , and HC10 4 
has already been discussed. 

In connexion with co-ordination the position of hydrogen is 
peculiar. In most of its compounds its stable valency group is two, 
as we should expect since this is the number in helium ; it attains 
this usually by forming a single covalency, but rarely, as we have 
seen, by direct transference of an electron, giving the negative ion 
[H]~. But there is strong evidence that hydrogen can form a larger 
valency group of four electrons. This must of course be pro- 
duced by co-ordination, the two extra electrons being borrowed 
from another atom. One of the strongest grounds for believing 
this is derived from the behaviour of hydrofluoric aeid. While 
the other halogen acids have the simple formula HX, as we 
should expect, hydrofluoric is undoubtedly polymerized, and 
even in the vapour state contains HgFg molecules, and higher 
polymers as well. The occurrence of a series of stable salts 
like KHF 2 indicates the same thing, and further shows that 
the polymer forms an anion [HF 2 ]~. This must be formed by the 
combination of a molecule H-F with a fluorine ion : the ion 
must share one of its lone pairs with either the fluorine or the 
hydrogen of the H F. It cannot be with the fluorine, since 
no other fluorides behave in this way, and we have reason to 
know that fluorine cannot have a larger valency group than 
eight. Hence the link must be formed with the hydrogen, which 
must take up, in addition to the pair of electrons which it already 

has, another pair from the fluorine ion, giving ; F ; H ; F | . 

The formula of the acid is thus H[F-vH-F]. This explains 
the polymerization, which indeed can proceed beyond double 
molecules, since we might have H[F->H F--H F] and so 
on : it also explains why the other halogen hydrides do not 
polymerize in. the same way : for it is found that elements always 

I f tend to show their highest covalency in combination with 

\ ^ fluorine. 

Another argument is derived from the behaviour of water. 
This polymerizes, as we all know, and especially forms at low 
temperatures a triple polymer, the large molecular volume of 
which (the cause of the expansion of water below 4 and on" 
freezing) indicates that it is a covalent compound, a View sup- 
ported by the examination of its crystal structure. Now there 
is no way of formulating a polymer of H 2 O with non-polar links 

Co-ordination of Hydrogen 


except by supposing that the oxygen of one molecule forms a 
co-ordinate link with the hydrogen of another, by which means 
of course any number of \>water molecules can be linked together : 

' H H 
I I 

H-O-Ek-0-H-O-H, &c. 

This conclusion, that hydrogen cm by co-ordination acquire 
a valency group of four, and so exerjV covalency of two, is very 
strongly supported by evidence f ^wholly different kind de- 
rived from organic chemistry, which 'will be discussed later 
(p. 147). It is of great importance, especially in relation to the 
association of liquids. J 



IT may be useful at this point to consider briefly what light the 
ideas of valency so far advanced throw on the connexion be- 
tween the chemical relationships of the periodic table and the 
theory of atomic structure. The form of the table already given 
(p. 89), which is best adapted to illustrate the Bohr theory of 
development, is less suitable for our present purpose. A more 
convenient classification of the elements into groups is scoured 
by using a slightly modified form of Mendele'eff's table, with 
its eight (now nine) groups and their subgroups, which also has 
the advantage of familiarity. The only important departures 
from Mendele"efP s scheme are the introduction of the inert gns 
group (Group O), and the inclusion of the whole of the rare Mirth 
metals (La 57 Lu 71) in Group III A. Every group exeept 
the first and last then has the same general form. Suppose we 
are considering the Nth group. In each of the two short periods 
(the ' period ' is taken to include, as in the Bohr scheme, all the 
elements between one inert gas and the next) it has one repre- 
sentative, the atom containing N more electrons than helium or 
neon : the first of these is commonly called the typical and the 
second the subtypical element, but we may conveniently use the 
word typical to cover both. In the three following periods (the 
two long periods and the rare earth period) each group has two 
representatives, the first of which is said to belong to the A and 
the second to the B subgroup. 1 Of these two the first (A) is 
characterized by having, like the typical elements, N more 
electrons than the inert gas at the head of the period (with a 
suitable modification in the rare earth period) ; the second (B) 
comes 8 - N places in front of the next inert gas. The whole 
of the chemical properties of the groups are determined by these 
structural relations. 

The most fundamental distinction has already been indicated. 
Owing to the exceptional stability of the inert gas structures, the 
neighbouring elements wiU always tend to assume them : hence 

1 It is unfortunate that the words ' group ' and ' subgroup ' are used 
m two different senses : of groups of electrons in an atom, and of groups of 
elements m the periodic table. Usually the context makes the meanimr 
clear ; wherever confusion seemed possible I have specified the sense in 
which the words are used. 












<N H 








r- CO 








oo o 










H S 








76 Valency and the Periodic Table 

the elements at the beginning of a period will so to speak look 
back, and those at the end will look forward : the former will 
tend to lose and the latter to gain electrons, and the number 
which they lose or gain will be the difference between their own 
atomic numbers and that of the neighbouring inert gas. This is 
the reason why the earlier groups are metallic or electropositive 
in character, giving positive ions, while the later groups are 
electronegative, and give anions, or obtain the necessary increase 
of electrons by means of covalent links : and also why there is 
the simple relation between the valency of an element and its 
group-number which Mendeldeff first pointed out. 

The properties of the elements are largely dependent on 
whether they can form simple ions or not, and whether these 
jons are positive or negative : the ' metallic character ' is essen- 
tially the power of forming positive ions. The conditions which 
determine ionization are primarily two. Firstly, the ion is more 
difficult to form the higher its valency : the removal or addition of 
each successive electron needs more work, owing to the resistance 
offered by the charge which the atom has already acquired. 
Secondly, the number of electrons which the ion still possesses 
must be capable of a stable arrangement. The most stable 
arrangements are of course those of the inert gases, and hence 
ions are most readily formed by elements only one or two places 
removed from an inert gas : indeed negative ions are only formed 
by such elements. But there are two other forms of electronic 
grouping which are stable enough to exist in cations. All the 
inert gases have an outer group of eight electrons ; but as we 
have seen, a structure in which this outer group is removed, and 
there is left an outer group of eighteen electrons, can have a very 
considerable degree of stability. Now in any group the ' com- 
pactness ', that is to say the tendency of the electrons to remain 
in that group instead of passing out into the next group of 
higher quantum number, increases with an increase of the 
electric field in which the electrons are moving that is, of the 
nuclear charge. We have already seen two examples of this. 
The nineteenth electron, which in K and Ca + (nuclear charges 
19 and 20) occupies a 4^ orbit, in Sc ++ (nuclear charge 21) is 
recalled to a 8-quantum orbit. In the same way the 18 group 
is only maintained as such if the nuclear charge is sufficiently 
large. Nickel 28 might form the groups (2) (8) (18), but we 
know that certainly one and probably two of the eighteen elec- 
trons go into the fourth quantum group, giving (2) (8) (16) (2). 

Monatomic Ions 77 

In copper the nuclear charge of 29 is sufficient to maintain the 
18 group, the structure being (2) (8) (18) (1), but it is only just 
sufficient ; chemical forces can easily remove one of the eighteen 
electrons, giving the cupric ion (2) (8) (17). In zinc 80 and in all 
higher elements the field is strong enough to maintain the 18 
group against chemical attack. Hence in all the seven elements < 
preceding an inert gas, or in all but the first of them, the group* 
of eighteen electrons is of sufficient stability to persist, and scl^ 
these elements show on the whole the same properties of ioniza-l 
tion and valency as the elements of the two short periods. But 
these are the elements of the B subgroups, and this is what 
justifies us in classing them in the same groups with the typical 

The third type of core which is stable enough to exist in ions 
is that in which the outer group is an imperfect one containing 
between eight and eighteen electrons : this occurs in the transition 
elements in the wider sense, those which are enclosed in frames 
in the Bohr table (p. 89). These elements all form cations, the 
valency of which (except in the third group) is always less than 
the group number. The stability of the core is sufficient, but is 
small enough to be open to chemical attack, so that one or two 
electrons can be removed from it. Hence these are elements of 
variable valency. Iron, for example, gives two kinds of ions, the 
structures being : 

Fe 26 = (2) (8) (14) (2) 

Fe++ 24 = (2) (8) (14) 

Fe +++ 23 = (2) (8) (18) 

These elements, it should be observed, form the A subgroups of 
the later periodic groups and the transitional triads of Mendele'eff. 
These principles enable us to understand the distribution in 
the periodic table of the elements which form simple 1 ions. 
Cations are known with valencies up to four (for example, the 
stannic ion Sn ++++ ), but no anions of a higher valency than 
two. The reason for this difference is obvious : whereas an in- 
crease in the positive charge on an atom binds the remaining 
electrons more firmly, an increase in the negative charge weakens 
their attachment. Even in a univalent anion, since there is one 

1 The question how far ions in solution are covalent (co-ordinated) com- 
pounds of the simple ions with the solvent is one of great complexity, which 
will be considered later. For the present we may disregard it, and treat, 
say, the aluminium ion as a simple ion Al +++ , whether in solution it forms 
a co-ordinated compound with the solvent or not. 

78 Valency and the Periodic Table 

more electron than is equivalent to the nuclear charge, if thi; 
is removed to a distance the rest of the ion being neutral has m 
force to call it back. Accordingly we find that no simple 
anions are formed except those which have the same number o 
electrons as an inert gas (hydrogen, the halogens, and oxygen 
sulphur, selenium, and tellurium). Such anions as Mn~ = (2 
(8) (8) (8) or Co~ = (2) (8) (18) cannot exist because these 
electronic structures are unstable, the first always unless all the 
last eight electrons are shared, the second unless the nucleai 
charge exceeds the number of electrons in the structure. 

Cations are more stable, and, for reasons which will be given 
in a later chapter (p. 104), their stability increases in any given 
group with the atomic number. Thus in the first short period 
only the first two members (Li, Be) form cations : in the second, 
the first three (Na, Mg, Al), but not silicon. A quadrivalent ion 
does not appear until much later, probably not before tin. No 
simple ions of a higher valency than four are known. In addition 
to these ions, all of which have the group valency, there are the 
ions of the transition elements in the wider sense, with valencies 
of two or three irrespective of their periodic group, which extend 
across the table to the end of the triads in Group VIII. 

It must be understood that the powers of ionization and of 
covalency-formation are not mutually exclusive. All elements 
other than the inert gases, even the alkali metals, can form 
covalent compounds under suitable conditions. In particular 
the last element in its period which is able to ionize positively (for 
example, beryllium or aluminium) is always peculiarly prone to 
form covalent links. It is also found that among the earlier 
groups the members of the B subgroups are more ready to form 
covalent compounds than theses/of the A : thus in the second 
group the halides of calcium s strontium, and barium are obviously 
more salt-like in character (less volatile and less soluble in 
organic solvents) than those of zinc, cadmium, and mercury. This 
is due to the fact already mentioned that the valency electrons 
of the B elements are moving in a stronger electric field (owing 
to the smaller stability and screening effect of the electronic 
group of eighteen) than those of the A elements, as is shown by 
the much smaller atomic volume of the former. 1 

Another fundamental characteristic of the periodic table is 
that in the earlier groups the typical elements resemble the A 
subgroup rather than the B, while in the later groups they 
1 For a further discussion of this see p. 104. 

A and B Subgroups 79 

resemble the B rather than the A. Thus in Group I lithium and 
sodium obviously form a closely allied series with the other alkali 
metals, while their affinities with copper, silver, and gold are slight. 
In the second group (Be, Mg : Ca, Sr, Ba, Ra : Zn, Cd, Hg) the 
differences are less marked, but still in the same direction. In 
the third group (B, Al : Sc, Y, La, &c. : Ga, In,' Tl) the typical 
elements are almost equally related to both subgroups : in the 
fourth carbon and silicon have more affinity with the B subgroup 
(Ce, Sn, Pb) than with titanium and zirconium ; and in the fifth, 
sixth, and seventh groups the resemblance of the typical elements 
to those of the B subgroup becomes increasingly marked, until 
in the last of these we have the halogens fromrfluorine to iodine 
forming an unusually well-defined series, while their resemblance 
to manganese is almost confined to "the similarity of the per- 
chlorates and permanganates, which one is inclined at first sight 
to regard as little more than accidental. 

These peculiar relations are a necessary result of the atomic 
structures, as can be seen by considering the stability of the 
respective atomic cores the groups of electrons other than the 
valency electrons. The typical elements contain completely 
stable and unalterable cores of an inert gas number (2 or 10). 
The elements of the A subgroups start (in Group I) with a 
similar core, but as the nuclear charge increases this becomes 
unstable, its outer electron group of eight beginning to expand. 
At first (for example, in scandium) these new electrons are easily 
removed and act as valency electrons, and the core is still for 
practical purposes that of the inert gas. But as they become 
more numerous in the later groups, they are increasingly difficult 
to remove ; the core expands, and a new set of properties begins 
to appear. This is why the A elements resemble the typical 
elements in the earlier groups but become less and less like them 
in the later. 

With the B elements the reverse process takes place. These 
have the group-number of valency electrons next to an electronic 
group of eighteen (mstead of eight). This group of eighteen is 
much less stable than a group of eight unless there is an excess of 
positive charge on the nucleus, or in other words, unless the 
element belongs to one of the higher periodic groups. Hence in 
the earlier groups the instability of the core in the B elements 
gives them properties different from those of the stable-cored 
typical elements : this is especially so in the first group, where 
the core can actually break down with the production of a higher 

80 Valency and the Periodic Table 

valency (Cu, Au), but in the following groups also (as in tl 
compounds of univalent copper and gold) there are marke 
differences due to the stronger field in which (owing to t? 
smaller screening effect of the 18 group) the valency electror 
are moving. As we reach the later periodic groups and tl: 
nuclear charge mcreases, the group of eighteen electrons is itsc 
moving in a stronger field and is therefore more firmly held 
its stability mcreases, and the resemblance of the elements to th 
typical increases likewise. 

The atomic structures also explain the peculiar nature of th 
increasing divergence in properties which occurs in the late 
groups between the typical elements and the members of th 
corresponding A subgroups. As we go along the series fo 
example, Sc, Ti, V, Cr, Mn the elements, instead of becomin 
increasingly electronegative, retain their metallic character ii 
the elementary state and in many of their compounds, in whicl 
they show valencies unrelated to those of the groups to whic] 
they belong ; but they also form a second set of compounds o 
an acidic kind, whose properties are consistent with their place 
in the table, and in these compounds they show the group va 
lencies. The reason can best be made clear by taking a particula 
instance, such as that of sulphur and chromium in Group VI 
Sulphur (2) (8) (6) can complete its octet, assuming the argoi 
structure (2) (8) (8), either by ionization (S~~) or by forming 
two covalencies as in H 8 S, where four of the electrons of th< 
octet are shared * (2) (8) (4, 2, 2). No such change is possible fo, 
chromium, because the corresponding structure (2) (8) (8) (8) i; 
unstable : the last group would break down, and some of it; 
electrons would go into the third quantum group, as happens ir 
Fe 26 = (2) (8) (14) (2). Again, by forming a co-ordinate 
link sulphur can become trivalent, as in diphenyl sulphoxidc 
( C 6 H 6 )2 S ->A in which it has the structure (2) (8) (2, 3, 3) 
This also is impossible for chromium, because the two unshared 
electrons of the last group would pass into the preceding group. 
leaving an incomplete octet. By means of a second co-ordinate 
link the sulphur, as we have seen, can become quadrivalent, as in 

sulphuric acid I> S ^ r di P hen y 1 sulphone 

1 The electrons of the octet are included in a bracket, the shared 
electrons being underlined. Thus (2, 8, 8) means that two of the eight 
valency electrons are unshared, and the rest (three pairs) are shared, 
forming three covalencies. See p. 164. 

Normal and Transitional Elements 81 

It now has the structure (2) (8) (4, 4). Here at last we have 
a structure which is possible for chromium. In chromic acid 

TT_Q/Cr^ it has the corresponding structure (2) (8) (8) (4, 4). 

The outer octet being wholly shared, there are no electrons 
free to revert to the preceding quantum group, and a stable 
atom results. Selenium (2) (8) (18) (6) will of course behave 
like sulphur. The resemblance between chromium and sulphur 
or selenium or generally between an A element of one of the 
later periodic groups and the corresponding typical element 
or B element, is only to be found m those compounds in which all 
the valency electrons of both are utilized with a valency of six 
in Group VI and of seven m Group VII because it is only then 
that the preceding electronic group of eight in the A element 
cannot attract any electrons out of the valency group and there- 
by destroy the stability of the structure. Thus it is not an 
accident, but a necessity of the case, that confines the analogy 
between chlorine and manganese to compounds of the type of 
the perchlorates and the permanganates, exactly as that of 
sulphur or selenium and chromium is confined to such compounds 
as the sulphates or selenates and the chromates. These are 
the compounds in which the element has the group valency. 

The structure of chlorine in perchloric acid ~ 

(2) (8) (4, 4), as that of manganese in permanganic acid 
H ~Q>Mn^Q is (2) (8) (8) (4, 4). The last group is wholly 

shared, and this leaves no electrons to disturb the stability by 
migrating to an inner quantum group. 

So far we have considered the properties peculiar to the 
typical or to the B elements, and those which they share with 
the A elements. The properties peculiar to the A elements 
(considering as before only the later periodic groups) are in 
particular the metallic characteristics, that is, the power of 
forming positive ions. An element like sulphur could only form 
a simple positive ion if it could lose all its six valency electrons, 
which, as we have seen, is impossible for any element : anything 
short of this would leave it with a highly unstable group of a 
small number of electrons ; for example, S ++ would be (2) (8) 
(4). The last four must remain in the third quantum group, be- 
cause the second quantum group of eight is incapable of expan- 
sion, and such a group of four would be too unstable to exist. 

Sofia M 

82 Valency and the Periodic Table 

No such difficulty arises with chromium. The four ' valency 
electrons remaining in Cr 4 * are all in the third quantum grouj 
(2) (8) (12) and a group of twelve in this position, with i 
nuclear charge of twenty-four, is quite sufficiently stable, al 
though by chemical action a third electron is very readily re 
moved, giving Cr +++ = (2) (8) (11). 

The eighth periodic group stands by itself, and has no resem 
blance in structure to any of those preceding it. It contains th< 
three transition triads Fe, Co, Ni : Ru, Rh, Pd : Os, Ir, Pt 
These are the elements containing eight, nine, and ten mort 
electrons than an inert gas, or in the third triad more than tht 
quasi inert gas number (2) (8) (18) (32) (8). Strictly speaking 
this group should perhaps be broken up into three : Group VIII. 
Fe, Ru, Os : Group IX, Co, Rh, Ir : Group X, Ni, Pd, Pt, so that 
i the group-number might still correspond to the excess of elec- 
trons over a stable number. But the importance of this excess 
in determining the properties of the elements is comparatively 
small. Except in a very few compounds such as Ru0 4 , OsO 4 , 
and OsF 8 they none of them exhibit the inert gas core : this has 
practically always expanded under the influence of the high 
nuclear charge, and the characteristic valencies are lower than 
the group-number would suggest. The elements belong essen- 
tially to the A class, and appear perhaps more peculiar than they 
really are, because there are no typical elements with which to 
compare them. 

Thus it is seen that the Bohr theory, in the light of what we 
have already learnt of the mechanism of valency, can explain 
some of the most fundamental chemical characteristics of the 
periodic table. There are many more which can only be ex- 
plained after a more detailed examination has been made of the 
various types of linkage, and the conditions of their formation. 
This therefore is the next subject which we have to consider. 


THE electronic structure which we assign to an atom in a 
molecule depends on whether we regard its attachments to 
other atoms as electrovalent or covalent, and no theory of the 
relation between structure and stability can be attempted until 
this question is settled. The distinction between the two kinds 
of covalency, normal and co-ordinate, is of less importance. The 
primary question is whether the attachment is due to the sharing 
of electrons, or to the electrostatic attraction of oppositely 
charged groups. In this chapter we shall consider the various 
criteria by which we can distinguish between these two forms of / 
link, and also the conditions which determine the conversion of [ 
one form into the other. The peculiarities of the co-ordinate 
link, the conditions of its formation, and the properties to which 
it gives rise, will be discussed later. 

While the existence of these two forms of valency is generally 
admitted, at any rate in extreme cases, there is less agreement 
on the question whether they are essentially distinct, or pass 
into one another by insensible gradations. The latter view is a 
natural deduction from the hypothesis of the static atom. In 
hydrochloric acid, for example, we may imagine a hydrogen ion 
gradually approaching a chlorine ion until ultimately the two are 
in contact : at the beginning of this process the attachment of 
the two is electrovalent, at the end it is covalent, and with a 
static atom there seems to be no reason for drawing an arbitrary 
line separating the two conditions. This is the view of G. N. 
Lewis, whose ideas were originally based on the cubic octet, al- 
though with the progress of physics he has come to accept the 
dynamic atom. But if we completely accept the implications of 
the Bohr atom, in which the electrons are moving in quantized 
orbits, it would seem to follow that a linkage must be either of 
one form or the other, and that the transition must involve a 
quantum change ; although in some cases this change may very 
well be brought about by a change of conditions, as for example 
of solvent, and there may even be substances which consist, in> 
the liquid or gaseous state, of a mixture of molecules of the two 
forms in equilibrium. 

This view, that electrovalency and covalency are essentially 

84 Eleclrovalency and Covalency 

distinct states of linkage, is strongly supported by various lines of 
argument which will be developed later, especially by the fact, em- 
phasized by Werner, that the covalency (co-ordination number) 
of an element is a characteristic of it in a series of compounds in 
which the electrovalency varies within wide limits (even with a 
change of sign) according to the nature of the covalently linked 

The differences in properties between electrovalent and co- 
valent compounds, which provide at once the justification for 
assuming the existence of two kinds of link, and the criteria for 
deciding to which class a given link belongs, may be grouped 
under two heads. 

I. In an ionized compound, though the oppositely charged 
ions are strongly attracted to one another, there is no real bond 
between them. They are free to take up any relative positions 
which are convenient, and as a rule will adopt a close-packed 
form. As this will under any given conditions be uniquely deter- 
mined (at any rate in the liquid or gaseous state), only one 
arrangement is possible, and isomerism is excluded. In covalent 
compounds on the other hand the linking orbits form part of the 
constitution of each of the atoms concerned. Their positions in 
space (relative to the other orbits) are thus fixed, and cannot be 
altered, beyond the limits of comparatively slight distortion, 
without a complete rupture of the orbit, that is, a quantum 
change. Hence covaiencifis, unlike electrovalencies, are directed 
forces, and it is quite possible to have the same groups arranged 
round the same atom in more ways than one : in other words, 
structural and stenc isomerism are possible only among groups 
whose constituent atoms are held together by covalent links. 

II. In a covalent compound the electrical forces are more or 
less completely satisfied within the molecule, and the external 
field offeree is small, whereas in an ionized molecule the electrical 
disturbance is greater, and there is a strong field of force outside. 
By an appropriate ' head to tail ' arrangement the molecules of 
an ionized compound can satisfy the attractions of this external 
field more completely. Hence the work required to separate the 
molecules is greater when they are ionized than when they are 
not. (We shall see later that co-ordinated molecules occupy in 
some sense an intermediate position in this respect.) 

All the methods used for distinguishing ionized from non- 
ionized molecules depend on the application of one or the other 
of these principles. 

Distinction in Properties 85 

The most obvious, the direct observation of ionization in 
solution, results from (I). Since the attachment of the ions is 
electrostatic, if we can dissolve the substance (without decom- 
position) in a medium of high dielectric power such as water, the 
ions will separate from one another, and can be detected by their 
conductivity. Werner, in his work on co-ordination compounds, 
was careful to establish the presence of electrovalencies in this 
way. It is also possible, by measuring the conductivity at 
various dilutions, to determine not only whether the molecule 
is ionized at all, but also how many ions it yields. The differences 
in velocity between ions other than hydrogen and hydroxyl are 
small, and so the absolute value of the conductivity gives, 
especially by comparison with other similar salts, a fan* indication 
of the number of ions into which the molecule divides. Further, 
Ostwald has shown that the change of molecular conductivity of 
a salt with dilution differs according as it gives two, three, or 
more ions, and is much the same for different members of any 
one of these classes, so that this magnitude also serves to show 
to which class a compound belongs. 

The usual methods of molecular weight determination in solu- 
tion, such as the cryoscopic, can also be employed to determine 
the degree of dissociation. Further, we can use any tests, 
physical or chemical, for the presence of the particular ions in 
question. Their concentration may be measured by means of the 
E. M. F. with a reversible electrode : this method is often used 
to determine the extent of the formation of the complex ion of 
a double salt, as in the complex cyanides, or the complex copper 
compounds of the hydroxy-acids. 

Any available chemical tests may also be used. Thus chlorine 
may be tested with silver nitrate, which will precipitate silver 
chloride if the chlorine is ionized, but not otherwise. In this way 
it was shown that in the three forms (two green and one violet) 
of hydrated chromic chloride all of which have the composition 
CrCl 3 , 6H 2 O, respectively one-third, two-thirds, and the whole 
of the chlorine is in the ionized state, giving the formulae 

Green form (1) Green form (2) 

[Cr(H 2 0) 4 Cl 2 ]Cl, 2H 2 ' [Cr(H 2 0) 5 Cl]Cl 2 , H 2 

Violet fdrm 
[Cr(H 2 0) 6 ]Cl 3 

Conversely, the presence or absence of silver ions in a solution 
of a double salt of silver can be detected by the action of an 

86 Electrovalency and Covalency 

alkaline halide. For example, the soluble silver sodium thio- 
sulphate Na[S 2 3 Ag] gives a precipitate with sodium iodide, but 
not with sodium chloride. This shows that the silver is almost 
wholly in a covalent state, but that the complex ion is to a 
minute extent dissociated, with liberation of silver ions. We can 
even calculate roughly the concentration of these ions. The 
solubility products at the ordinary temperature are approxi- 
mately : AgCl l<r 10 , Agl 10~ 16 . Hence if the halide used is 
decinormal, the normality of the silver ions lies somewhere 
between 10" 9 and 1CT 16 . 

These direct tests for ionization can only be applied to a sub- 
stance which is SQlubLe without decomposition in an ionizing 
solvent (practically always water) : they obviously could not 
be used with silicon tetrachloride or phosphorus pentachloride. 
Even when the compound is more stable and is not obviously 
decomposed by water, a reaction may take place. Complex ions 
may dissociate to some extent into their simpler components : 
thus the fluosihcates will give reactions for fluorine ion. Simi- 
larly covalent chlorine maybe replaced by hydroxyl or water 
(hydrolyzed) ; the second green form of chromic chloride slowly 
changes on standing in solution into the violet form, and all the 
chlorine can then be precipitated by silver. Such changes can 
usually however be detected when they occur, and so do not 
invalidate the ionization tests where these give definite results ; 
but they limit their application very seriously. 

A conclusive proof of the presence of covalent links, but one 
which is even more limited in its application, is the existence of 
isomerism, and especially of stereoisomerism. If a molecule is 
optically active, although the groups attached to the central 
atom are not, we may assume that they are covalently attached. 
Any ionized groups, smce they are not 'joined by directed forces 
to the central atom, must take up positions uniquely determined 
by the other atoms in the molecule : there cannot be two alter- 
native positions possible for them. The same arguments apply 
to isomerism in general, provided that it can be shown to occur 
in the liquid or dissolved state ; the same individual molecules 
can sometimes take up several different crystalline arrangements. 
These tests are of course limited to particular kinds pf com- 
pounds. But if we find, for example, that those six co-ordinated 
chromium compounds whose structure would admit of optical 
activity if the six groups were covalently linked, do actually 
exhibit this activity, we can infer not only that the links are 

Evidence from Volatility 87 

covalent in these compounds, but also that they are so in other 
inactive compounds of the same general type. 

Where these criteria fail we have to rely on other and less 
precise tests. These are often quite sufficient when our object 
is to determine not whether a complex salt dissociates into two 
or into three ions, but whether a substance is a salt at all. We 
can then make use of any of those properties which distinguish 
a salt from a covalent compound. 

The most obvious of these is the volatility. As we have seen, 
one characteristic of ionized molecules is that, as they have 
stronger external fields of force, they are more strongly attracted 
to one another than covalent molecules, and more work is re- 
quired to separate them. The boiling-point of a substance is 
lower, the less the thermal agitation required to overcome the 
mutual attraction of the molecules. It is simply related to the 
work of separation (heat of evaporation), as is seen from Trou- 
ton's rule that the molecular heat of evaporation is approxi- 
mately twenty-one times the boiling-point in degrees absolute. 
This rule does not hold for substances with very low boiling- 
points like helium and hydrogen, and only roughly for the 
' permanent ' gases ; but for other substances it gives a fair 
approximation, except for highly associated liquids like water 
(25-9) and ethyl alcohol (26-9), where the molecular weight is 
uncertain. Generally speaking, we may take it that the heat of 
evaporation of a substance boiling at 0C. is 6, at 100 is 8, at 
500 is 16, and at 1000 is 27 kilogram-calories per gram-mole- 
cule approximately. 

Hence a covalent compound will in general have a lower 
boiling-point than a salt. The most striking example of this is 
given by the hydrides of the elements. With the exception of 
a few hydrides of transition elements, such as palladium, copper, 
cerium, &c., whose chemical individuality is doubtful, the binary 
hydrides fall sharply into two classes. 1 All the nineteen known 
elements one, two, three, or four places before an inert gas, and 
also boron (but nothing telse)'forni hydrides which are volatile and, 
so far as they have been examined, practically non-conducting, 
like methane : these are obviously covalent compounds. On the 
other hand the alkali metals and those of the alkaline earths form 
non-volatile hydrides, which are good conductors in the fused 
state, and on electrolysis liberate hydrogen at the anode, showing 
that they are salts containing the negative hydpgen ion. 
1 Paneth, Ber. 1920, 53, 1710. . 

88 Electrovalency and Covalency 

The halides of the elements show a similar differentiation into 
volatile non-salts and non-volatile salts. The two classes differ 
not only in the absolute values of the boilmg-points, but also in 
the effect on the boiling-points of the replacement of one halogen 
by another. A metal such as sodium forms halides which are 
typical salts : and these have very high boiling-points which fall 
slowly as the atomic weight of the halogen increases. The halides 
of non-metals such as carbon or silicon have comparatively low 
boiling-points, but these rise rapidly as the atomic weight of the 
halide increases. The following table gives some examples : 


NaF NaCl NaBr Nal 

1695 1441 1308 1300 . 

SiP 4 ' SiC1 4 SiBr 4 SiI 4 - 

- 90 -(- 57 . 153 ca. 290 

A1C1 3 \ AIBr 3 A1I 3 

1 ca. 800 183 a \ 260 35o' 

SnF 4 ' SnCI 4 ' SnBr 4 SnI 4 

''705 114 203 300 

This sharp difference in properties indicates an equally sharp 
distinction in structure, and it is evident that the compounds of 
the first class (high boiling-points, falling from F to I) are salts, 
while those of the second are covalent. The opposite effect of 
a change of halogen in the two classes is what we should expect. 
The volatility of a normal substance is less the greater the mole- 
cular weight, and hence in the non-polar halides the boiling- 
points will rise as we go from the fluoride To^jk^lo^lde. But in 
the salts the determining factor is the electro^ws^j^ttr^jtion of 
the charged ions, and as the charges are tike s%ne this force 
t'must diminish as the atomic diameter of the haltfgefr indftases. 
The absolute boiling-points of the sodium salts arejrqughly in 
inverse ratio to the distances between the a-romic centres, infche 
crystals, as determined by the Braggs from X-ray iftA&sure*n.ents. 

It will be observed that with elements of an impfirffectlV 1 metal- 
lic character, like aluminium and tin, we do not fin fh^fc the 
halides as a whole are intermediate in properties between the 
two classes, but that the fluorides clearly belong ,^o*the salt 
class, while the chlorides, bromides, and iocndes have the 
normal behaviour of the covalent class, the boiljfig-points being 
fairly low, and rising rapidly with the rise in atomic weight of the 

Evidence from Volatility 89 

It is thus a general characteristic of ionized compounds to be^^ 
non-volatile, and of covalent molecules to be volatile. With 
many compounds however the volatility cannot be observed 
directly, because they decompose below the temperature at 
which the vapour pressure becomes measurable. For such sub- 
stances a qualitative estimate of the ionization or otherwise may 
often be arrived at through the solubility. This question cannot 
be fully discussed until we have dealt with the properties of 
associated liquids, which involves a more detailed examination 
of the co-ordinate link. But this much may be pointed out. 
The mutual attraction between the molecules of a solid salt, 
which diminishes its volatility, will also tend to lower its solu- 
bility. But a solvent of high dielectric capacity like water will 
diminish the forces between the ions by lowering their potential ; 
and it can further promote solution by combining with the ions. 
This is why we find salts (like sodium chloride, B.Pt. 1441) 
which are very soluble in water, although their vapour pressure 
at the ordinary temperature must be infinitesimal, and their 
melting points are very high. But a solvent of low dielectric 
constant and saturated character like a hydrocarbon (D.E.C. 
about 2, while that of water is 81) has but a very slight electrical 
and no chemical effect : it therefore cannot overcome the 
attraction of the ions, and salts, as we know, are in general in- 
soluble in hydrocarbons. Hence if we find that a substance will 
dissolve fairly readily in such a solvent as benzene, we may 
assume that Jt^is not ionized. 

There is one caution which must be borne in mind, in con- 
sidering lobtyt J&e^omtility and the solubility. These properties 
are diminished B^the presence of electro valencies, but they are 
also diminished; fof obvious reasons, by an increase in molecular 
weiglfc, aTgd therefore by polymerization or association. The 
effect these changes in ordinary cases (where only a few mole- 
cuJfes aty so pombmed), though perceptible, is not great enough 
to bg i5st^t:en for that of ionization. For example, in the table 
of Doiling-fidfaits on p. 88 it will be seen that those of the 
aluaffipfjjjft] compounds are, apart from the fluoride, higher than 
those o| pie tiat compounds, although the formula-weights of the 
latter afe greater. This is due to the polymerization of the 
aluminium halides, of which the true formula at the B.Pt. is 
Al a X 6 . But^be resulting elevation of the boiling-points is not 
comparable with that which ionization would produce. 

On the other hand, there are certain substances of which the 

3<* N 

90 Electrovalency and Covalency 

whole crystal forms one great molecule, with all its atoms held 
together by covalent links. Of these ' giant molecules ' (Riesen- 
molekule) the best-known examples are diamond and carborun- 
dum CSi. Such a molecule has, properly speaking, no vapour 
pressure or solubility : it can only melt or boil by actually dis- 
sociating, and owing to the firmness of the linkages this usually 
requires a very high temperature. These substances might easily 
be mistaken for ionized compounds : their non-polar character 
can only be ascertained by examination of the structure of the 

lonization and Crystal Structure. 

This brings us to the question how far the nature of the 
linkages can be established by the determination of the crystal 
structure by X-ray analysis. This appears to be, and no doubt 
will become, a very fruitful field : but at present the results have 
to be treated cautiously. It is only in the simpler forms of 
crystal that they afford much help, and the interpretation of the 
data from this point of view is only beginning. With the simpler 
inorganic salts, such as sodium chloride, we have direct evidence 
of lonization in the solid from the phenomenon of residual rays 
(Reststrahlen) of Rubens. The atoms of a crystal have their 
natural frequencies of vibration, and if they are charged if 
the crystal forms an ionic lattice these vibrations will cause 
an abnormally high reflection of incident light of the same fre- 
quency, by a direct process of resonance (not a quantum ex- 
change). The actual frequencies are far in the infra-red 1 (with 
sodium chloride about 50ju or 500,000 A.U.), and the phenomenon 
can be detected by allowing a beam of infra-red rays from a 
heated body to suffer repeated reflection from the surface of the 
crystal, when the other wave-lengths are absorbed, and those 
corresponding to the characteristic frequencies survive. These 
results make it certain that the salts examined are ionized even 
in the crystalline state. 

But the usual method of examining crystal structure is by 
means of X-rays, a method originated by Laue, and developed 
especially by W. H. and W. L. Bragg and by Debye. It consists 
essentially in using the crystal as a diffraction grating, with rays 
of known frequency, and so determining the distances between 
the reflecting centres of the crystal lattice itself. The rays must 

1 Rubens and v. Wartenberg, Sitzb. K. preitss. Akad. 1914, 169 ; cf. 
Fosterling, Ann. d. Phys. 1920, 61, 577. 

Evidence from Crystal Structure 91 

be of the same order of wave-length as the distances between the 
atoms of the crystal (a few A.U.), and so X-rays must be used. 
It can be shown that the reflection is due to the electrons and not 
to the nuclei of the atoms. It was at one time supposed that 
the number of electrons in the atom could be determined in this 
way from the intensity of the reflections, and that the results 
obtained with lithium fluoride proved that the lithium atom had 
two and the fluorine ten electrons, indicating the transference of 
an electron by ionization. Later work has made it doubtful 
whether the results are accurate enough to justify this inference. 
There is no doubt however that the X-ray method gives us, 
even with salts of considerable complexity, an accurate picture 
of the disposition of the atoms in the crystal, from which valuable 
conclusions can be drawn as to the nature of the linkage be- 
tween them. 

In the simplest cases of the alkaline halides two types of struc- 
ture occur, known as the rock salt and the 'caesium chloride 
lattices. In the first each sodium atom is surrounded symmetri- 
cally by six chlorine atoms, and each chlorine by six sodiums : 
the second is similar, except that the number is eight instead of 
six. These structures are exactly what we should expect if the 
atoms of the lattice are really ions, with no attachment to one 
another beyond their electrostatic attractions. ^ They are close- 
packed systems, and there is no indication that a particular sodium 
atom is more closely linked to one chlorine than to any of the 
other five. In a crystal like calcium carbonate we find the same., 
kind of relation between the calcium ion and the CO 3 ion, bur 
a different one for the constituent atoms of the CO 3 group itself : 
here the three oxygen atoms have a relation to one another and ' 
to their own carbon different from that which they have to those ' 
of any other CO 3 groups ; and this may be taken as evidence that 
the calcium and the CO 3 are themselves ions, but that the atoms 
of the C0 3 group are covalently linked to one another. Similar 
results have been obtained with more complex compounds. In 
NiCl 2 , 6NH 3 it has been shown that the six ammonias are ar- 
ranged symmetrically (at the points of an octahedron) round the 
nickel : an identical arrangement of the six chlorine atoms round 
the platinum has been observed in ammonium platmichloride, 
and of the six water molecules round the zinc in zinc bromate 
hexahydrate. We may therefore assume in these salts complex 
ions whose atoms are covalently united, as indicated in the 
formulae [N^NEgjCl-j, (NH 4 ) a [PtClJ, and [Zn(H 2 O)J(BrO 3 ) 2 . 

92 Electrovalency and Covalency 

When we find that a molecule has an elaborate and open struc- 
I ture, occupying a large volume, we may assume that the linkages 
are covalent, or the parts would be more closely packed. This is 
what happens with ice, 1 which has a very diffuse molecule, 
apparently of the formula H 6 O 3 . 

This line of argument has recently been developed with great 
ingenuity by Grimm and Sommerfeld. 2 They have classified the 
crystal structures of all compounds hitherto examined of the 
general formula AB (1 : 1 compounds of two elements) in which 
an atom of A and one of B have eight valency electrons between 
them. They find that four types of lattice occur : the rock salt 
and caesium chloride types already mentioned, with each A 
surrounded by six or eight B and vice versa, and the diamond 
and wurtzite (ZnS) types, which both have four A atoms arranged 
round each B at the points of a tetrahedron. These two latter 
forms are not close packed, and the authors conclude that where- 
as the first two types (rock salt and caesium chloride) represent 
ionic lattices, the last two are covalent, and the crystals in these 
cases (e.g. carborundum CSi, A1N, and even BeO) are ' giant 
molecules ' in which all the atoms are joined by shared electrons. 
Where A and B belong to different periodic groups, we must sup- 
pose that the eight electrons are first divided equally between 
them, giving four to each atom, which are used to form four co- 
valencies : so that in a sense we may say that the formulae 
should be written A1~N + and Be"O f+ , although the atoms 
are not ions, but are covalently linked throughout the crystal. 
The results of this work will be considered in more detail later. 

The Transition between Electrovalencies and 

As we have seen, there is good evidence that some molecules, 
like those of sodium chloride, are always ionized, even in the 
solid, and that others, such as methane, are never ionized, but 
always held together by the sharing of electrons. But with many 
substances the evidence is that in some states they are ionized, 
and in others they are not. Examples of this are found among 
the halides of the polyvalent elements. Stannic chloride, for 
instance, is a volatile liquid miscible with benzene, and is a non- 
conductor of electricity. In the absence of hydroxyhc solvents 

1 W. H. Bragg, Proc. Phys. Soc. 1922, 84, 98. 
a Z.f. Physik, 1926, 36, 86. 

Conditions of Transition 93 

it has all the characteristics of a covalent compound. But in 
water it is evidently ionized, and gives the reactions for stannic 
and chlorine ions. We cannot but conclude, in spite of its be- 
haviour in water, that in the pure state and in non-ionizing sol- 
vents it is a covalent compound. It is quite possible to argue 
that strictly speaking SnCl 4 is always covalent, and that what 
is formed when it is dissolved in water is an ionized compound 
with the solvent, such as [Sn(H 2 O) fl ]Cl 4 , which is certainly the 
composition of the solid which separates from the water. This 
however is of secondary importance ; the main point is that 
a substance which when dissolved in water undoubtedly gives 
rise to ions, may in the absence of water be a non-polar com- 
pound. The trivalent chlorides of aluminium and iron behave in 
the same way : they are volatile (at least in comparison with an 
alkaline chloride), they dissolve in hydrocarbons, they are non- 
conductors, and generally in the absence of water they show the 
properties of covalent compounds. In water they give chlorine 
and aluminium or ferric ions, and the salts which separate con- 
tain in both cases six molecules of water of crystallization. Here 
again it is very probable that the combination with the water 
renders the ionization possible. A similar instance is that of the 
halogen hydrides. These with the exception of the polymerized 
hydrogen fluoride are gases of low boiling-point, do not conduct 
in the pure liquid state, and are soluble in hydrocarbons. If their , 
behaviour in dissociating solvents were unknown, no one would > 
doubt their covalent character. But in water they are of course 
practically completely dissociated into their ions. 1 

For these reasons it is clear that a molecule can pass from the , 
ionized to the covalent state and vice versa, with a suitable /' 
change of conditions. 

Weak Electrolytes. 

A more difficult question is whether, when a substance is dis- 
solved in water and partly dissociated into ions, the non-dis- 
sociated portion is wholly held together by electrovalent links, 
or whether it forms an equilibrium mixture of non-dissociated 
ionized molecules and covalent molecules, as represented by the 
equation [R]A ; R A, or is wholly in the latter (covalent) 
form. 2 

1 Compare Biltz and Klemm, Z. anorg. Chem. 1926, 152, 267. 

2 The terms ' dissociated ' and ' ionized ' are commonly used in the 
discussion of electrolysis as if they were synonymous ; but now that we 

94 Electrovalency and Covalency 

With strong electrolytes this question does not necessarily 
arise. The recent theory of Debye explains satisfactorily the 
' anomaly ' of strong electrolytes without needing to assume any- 
thing in the solution except the two kinds of ions at varying dis- 
tances from one another, and finds the cause of the difference 
between the change of conductivity with dilution and the 
law of mass action essentially in the fact that the electrical 
forces between ions act over longer distances than the chemical 
forces between neutral reacting molecules. It is commonly said 
that this theory involves the complete dissociation of the strong 
electrolyte. It would perhaps be more correct to say that it 
involves its complete ionization (which is indeed already estab- 
lished for salts like the alkaline halides by the determination of 
the crystal structure and the observation of the ' Reststrahlen ' 1 ), 
and that it abolishes the distinction assumed by Arrhenius be- 
tween a dissociated portion, in which the opposite ions were 
without action on one another, and an undissociated portion, in 
which they were in contact ; the truly undissociated (but still 
ionized) part now appears as a limiting case, in which the distance 
between the opposite ions is reduced to a minimum. The appa- 
rent fall in the ionization of a salt (whether this is measured by 
the conductivity or the osmotic properties) is adequately ac- 
counted for by the restraining influence of the ions on one 
another, due to their electrical charges. 2 This causes a strong 
electrolyte, which is completely ionized and practically com- 
pletely dissociated, to have at moderate dilutions a molecular 
conductivity which (for a uni-univalent salt) is something like 
80 per cent, of that at infinite dilution. It is difficult to imagine 
that the size of the ions, or the nature of the electrolyte (so long 
as it is completely ionized, and we are dealing solely with the 
electrical forces between the ions) can greatly affect this ratio ; 
indeed it has been shown that for normal salts it is almost 
wholly determined by the valency of the ions, being in deci- 
normal solution for a salt M'X' 84 per cent., for M // X 2 ' 74 per 
cent., and for M"X" 40 per cent. in all cases within two or three 

recognize two forms of linkage it is clear that an undissociated molecule 
may be either ionized (electrovalent) or covalent. 

1 p. 90. 

2 This does not exclude the possible presence of a minute concentration 
of non-ionized (covalent) solute, where there is independent evidence of 
its existence : as in certain strong acids like hydrochloric, which have a 
measurable vapour pressure in aqueous solution. 

Weak Electrolytes 95 

units, whatever the salt examined : and these values are in 
accordance with the Debye theory. 

But when we come to weak electrolytes, we find that the 
apparent dissociation (however it is measured) is of a different 
order of magnitude. Moreover it is a remarkable fact that while 
some acids and bases are strong and others are weak electrolytes, 
salts are strong electrolytes, whether the acids and bases from 
which they are formed are strong or weak. Ammonium acetate 
has nearly the same apparent ionization as sodium chloride, 
although both ammonia and acetic acid are weak. To put it in 
figures, the molecular conductivities of sodium chloride, sodium \ 
hydroxide, hydrochloric acid, and ammonium acetate at moderate 
dilutions are all about 80 per cent, of the values at infinite 
dilution, while those of acetic acid and ammonia are only about 
1 percent. 

This strongly suggests that an electrovalent link is always dis- 
sociated in water to about the same almost complete extent : 
that if only the ionized form is present we shall always find the 
apparent ionization in a normal solution to be some 80 per cent. : 
and that the low conductivity of weak electrolytes is due to two 
forms being present in the solution in equilibrium, an electro- 
valent and a covalent form, the first being dissociated to the 
same extent as a strong electrolyte, but being present only in 
small quantity. For example, m normal acetic acid, where the 
conductivity indicates a dissociation of 0-4 per cent, we might 
have 99 5 per cent, of the acid in the covalent form [CHg CO OH], 
and 0-5 per cent, in the electrovalent form [CHg CO 0]H, with 
a molecular conductivity four-fifths of that at infinite dilution. 
The position of the equilibrium between these two forms will 
obviously depend not merely on the charges of the ions, but on 
their chemical nature. Now this feeble ionization is confined 
(with the exception of the salts of a few metals, such as cadmium 
and mercury, which will be considered later) to some inorganic 
and most organic acids, and many organic bases, including 
ammonium and phosphomum hydroxides. If our theory is 
sound, there must be some reason why substances of these 
kinds are peculiarly easily able to pass from the electro- 
valent to the covalent state, and some evidence from their 
physical and chemical properties that they do so. 

Taking first the acids, we have to explain why they have a 
tendency to assume the covalent form which is lost when the 
acidic hydrogen is replaced by a metal. Now G. N. Lewis has 

96 Electrovalency and Covalency 

pointed out that hydrogen occupies a peculiar position in that 
the number of electrons which the hydrogen ion needs for stabi- 
lity is two, which is the precise number that it gains when it 
passes from the ionized to the covalent state : 
H+ + :X- > H : X 

But a metallic ion needs eight, and the condition of a metallic 
ion to which only two shared electrons have been added (as in 
sodium ethide) is excessively unstable. Hence the transforma- 
tion into the covalent link will be far easier with hydrogen than 
with metals, and acids must have a power of changing into the 
covalent form which is in general denied to salts. 

Again, it has been known for some time that the order of 
strength of acids is quite different in other solvents from what 
it is in water, and that the difference cannot be explained by the 
electrolytic theory alone ; for example, the strength of per- 
chloric, hydrochloric, and nitric acids in water is about the same, 
all three being highly dissociated, while in ether (as measured by 
their chemical activity) it is roughly in the ratio 100 : 1 : 0. 
Hantzsch has recently 1 argued in great detail in favour of this 
view, that all acids have the power in varying degrees of passing 
(for example, with a change of concentration or solvent) from 
a polar to a non-polar form. He supports this by evidence drawn 
from a very wide range of phenomena, especially the change in 
absorption spectrum and in chemical properties as the solvent 
is varied. He finds that these properties on the whole go to- 
gether ; the absorption spectrum .of the acid is as a rule inter- 
mediate between that of its salts and that of its esters, and 
inclines towards the ester type under conditions where the 
chemical properties indicate a predominance of the covalent 
form. These conclusions are supported by the general behaviour 
of weakly acidic organic compounds such as carboxylic acids and 
especially alcohols and phenols, which under conditions that do 
not favour dissociation is that of covalent rather than that of 
undissociated electrovalent compounds. This is what we should 
expect if they exist in two quasi tautomeric forms, one electro- 
valent and the other not. 

This view is strengthened by the behaviour of the ammonium 
bases. We all know that ammonium hydroxide is a weak base 
1 Z.f. Elektrochem. 1928, 29, 221. His arguments have been attacked 
by v. Halban (ibid. 434), who has certainly weakened the force of some of 
them. But even so the balance of evidence seems to be clearly on Hantzsch's 

Weak Electrolytes 97 

(of the same strength as acetic acid), and that the replacement 
of the hydrogens by methyl or ethyl groups increases its strength, 
but not very greatly until all four have been replaced, when we 
arrive at [NAlk 4 ]OH, which is almost as strong as caustic 
potash. This sudden increase of strength from that of a weak 
to that of a strong electrolyte on passing from a tertiary to a 
quaternary compound was formerly explained by the very 
natural supposition that the equilibrium 

NRj, + H 2 ^ NR 3 HOH (R = H or alkyl) 

which must obtain in a solution of ammonia or an amine, lies 
very far on the side of the anhydrous amine ; so that in triethyl- 
amme, say, there is in solution a very small quantity of the highly 
dissociated NEt 3 HOH and a large proportion of NEt 3 , producing 
the effect of a rather weak electrolyte ; while in the quaternary 
compound NR 4 OH, the dissociation to the tertiary amine being 
impossible, the full strength of the ammonium compound is 
exhibited. This view (which still survives in some quarters) was 
upset some time ago by Moore and Winmill, 1 who showed that 
it was possible, by measuring the conductivity of the base and 
also its partition between water and another solvent at several 
temperatures, to determine the amount of the free unhydrated 
amine in the solution, and hence the true dissociation constant 
of the ammonium hydroxide. The values which they obtained 
for this constant are given in the following table ; that for the 
quaternary hydroxide, which is added for comparison, is of 
course only rough, as the compound does not obey Ostwald's law. 

NH 4 OH NRH 3 OH NR 2 H 2 OH NR 3 HOH NR 4 OH 
R = CH 3 294 ,. 4-87 14 21 72 ca 10,000 

R = C 2 H 5 294 " 6 73 10-39 7-87 ca 10,000 

It is thus clear, not only that the effect is much less regular 
than was previously supposed, but also that the introduction of 
the fourth alkyl group makes an enormous difference in the 
strength of the base, which becomes of quite another order. 
Thus the current explanation of the fact that the tertiary amines 
are weak bases and the quaternary strong was disproved, and 
the real cause of the difference was still to seek. 

If we accept the view that a weak electrolyte exists in solution 
largely in a covalent form, ammonium bases like [NR 3 H]OH 

i J. C S. 1907, 91, 1378 ; 1912, 101, 1635. 

3061 O 


Covalent Links 

must be able to pass over into such a form ; but the change must 
involve a hydrogen attached to the nitrogen, since the base re- 
mains weak so long as one such hydrogen is present, but becomes 
strong (i.e. the covalent form vanishes) as soon as the last hydro- 
gen is replaced. This can only mean that the hydroxyl forms 
a covalent (co-ordinate) link with this hydrogen 


3\ / 



CH 8 


+ [0-HT 

CH 3 
CH 3 


We know that hydrogen can sometimes assume a covalency of 
two ; and though there is not much evidence of its doing so in- 
ordinary cases when it is attached to nitrogen, it is obvious that 
in this reaction the electrical charges will greatly promote the 
change. When all the hydrogens are replaced this change is no 
longer possible, since we have evidence that hydrogen atoms in 
an alkyl group have not this power. 1 

In this way the theory that a weak electrolyte consists of a 
covalent and an electrovalent form in equilibrium enables us to 
account for the peculiar behaviour of the nitrogen bases. 

Orbits of Shared Electrons. 

The question of the real meaning of the ' sharing ' of electrons 
has so far been left open. It is an obvious suggestion that as 
a ' lone ' electron encircles one nucleus, so a shared electron 
encircles two, though perhaps all that we are entitled to say 
at the moment is that its orbit is related to the two nuclei. The 
chemical evidence does however go far to show that the relation 
to both nuclei is the same in character : that such an orbit is not 
merely the orbit of the unshared electron somewhat distorted by 
the presence of the second nucleus, but that it actually forms 
part of the system of orbits of both atoms, and as far as we can 
see in the same way. We may therefore assume that while the 
shared electron is hi the neighbourhood of each nucleus, its orbit 
is of the same general kind as those of the unshared electrons of 
that nucleus. This would explain why such an electron counts 
as one towards the stable electron number for each atom. 

Now 2 on the Bohr theory the elliptical orbits (which most of 
the valency electrons occupy) consist essentially of two parts : 

1 This explanation of the behaviour of the amines was put forward by 
Latimer and Rodebush, J. Amer. Chem. Soc. 1920, 42, 1419. 

a Cf. R. H. Fowler, Trans. Faraday Soc. 1928, 19, 459. 

Orbits of Shared Electrons 99 

(1) inner loops, in which they come near the nucleus, and the 
attraction of the latter being great, move with a high velocity ; 

(2) outer loops, in which they are far from the nucleus and move 
much more slowly. For the maintenance of the stability of the 
atom the important part of the orbit is the inner loop, and the 
essential point is that the various electrons of a subgroup should 
pass through this loop in the right directions in space, and in due 
succession in time. In the outer loop their motion is less impor- 
tant, provided they return to the inner loop after the proper 
interval. Hence there seems to be no difficulty in supposing that 
the electron having gone through the inner loop round one 
nucleus might go over and perform the same service for the 
other : in which case it would count as an electron for each. We 
may also suppose that of the two electrons forming the covalent 
link one will be near one nucleus when the other is near the 

This will also account for the fixed positions in space occupied 
by the attached atoms, since the planes of the linking orbits will 
be definitely related to one another. We can also see that if the 
structure of the molecules causes these atoms to be displaced 
from their natural positions, this will cause strain and instability 
in the molecule, as the Baeyer theory of strain demands. A fur- 
ther deduction from this idea relates to double links. Chemical 
evidence shows that two singly linked atoms can rotate (with 
their attached atoms or groups of atoms) round the line joining 
their centres so as to take up the most stable configuration, so 
that a compound of such a formula as H^C CXH a can only 
occur in one form : but that with two doubly linked atoms, as 
in HXC=CXH, this no longer possible. It is evident that 
if in such a double link we have four electrons shared between 
the two atoms, their orbits must start out from one atom in 
planes inclined at the normal angle. This means that the rela- 
tion between two doubly linked atoms is of the same kind as that 
between two atoms forming part of a ring ; and free rotation 
is as impossible in one case as in the other. 

In general terms, then, the conception of binuclear orbits 
seems to fulfil the necessary requirements. But when we try to 
enter into details we meet with great difficulties. The physicists 
are only beginning to learn how to deal with the dynamics of 
such systems, 1 and no satisfactory theory has yet been given 
even of the simplest of them, the hydrogen molecule. In these 
1 Cf. Niessen, Physikal. Z. 1926, 27, 299. 

100 Covalent Links 

circumstances the fewer assumptions the chemist makes, the 
better ; and for our purposes little more is required than to 
suppose that a shared electron counts as part of the constitution 
of both atoms, and that its orbit is in general similar to those of 
the unshared electrons, but with some differences ; of the effect 
of these differences on the stability we may hope to learn some- 
thing from an examination of the chemical evidence, but for a 
dynamical explanation we must wait until the physical and 
mathematical difficulties have been overcome. There are, how- 
ever, certain considerations which deserve attention. 

I. The second quantum number k of the Bohr notation is a 
measure of the energy of precession of the orbit round the 
nucleus. An orbit encircling two nuclei could only precess if the 
second nucleus moved with it, and the mass makes this impos- 
sible. Hence the Bohr system of notation cannot be applied to 
the orbits of shared electrons. How this difficulty is overcome 
how the successive loops, which in an isolated atom cut one 
another, become, with the shared electrons, superposed we do 
not know : it may possibly be due to a correlated oscillation of 
the nuclei. The attempt to explain it by assuming a figure-of- 
eight shape for the orbits is not dynamically satisfactory : this 
may be the correct form of the orbits (or of some of them), but 
it cannot be made to give the equivalent of the required pre- 
cession. Whatever the explanation may be, we obviously can- 
not specify the orbit in terms of its precession when there is 
none. Hence it is not legitimate to assign quantum numbers on 
the Bohr system to the shared electrons : we know their quan- 
tum numbers before they are shared, but these (or at least one 
of them) have no meaning after the covalent link has been 
established. This conclusion disposes of a good deal of argument 
which has been based on an assumed knowledge of these num- 
bers. Two remarks may be made here. 

(a) The close similarity in valency properties between suc- 
cessive members of the same periodic group (for example, chlo- 
rine, bromine, and iodine) indicates that the capacity of a ' lone ' 
electron to become shared depends on its second (and third) 
rather than on its first quantum number : for in these elements 
the valency electrons have the same second and third quantum 
numbers, but the first is three in chlorine, four in bromine, and 
five in iodine. 

(6) The octet, as we know, is an extremely stable group of 
electrons, not only when it is unshared (as in the inert gases), 

Orbits of Shared Electrons 101 

but also when it is completely shared, in four-covalent atoms 
(further evidence of this will be given later). When it is un- 
shared it consists of 2 xN 11} 2 xN 21 , and 4 xN 22 electrons : 
of these subdivisions the last two resemble one another much 
more closely than they do the first, so that for many purposes we 
may divide the group into two subgroups of two and six electrons 
respectively (this is on the system of Stoner and Main Smith : 
in the original Bohr theory there were four electrons in each sub- 
group). In the fully shared octet all that we know is that the 
eight electrons are in four pairs ; there must be some close rela- 
tion between the orbits of the two electrons of a pair, since they 
both enclose the same two nuclei, but that is all that we can say 
of them. There is no indication whatever of any difference 
between one pair and another, and so it seems very unlikely that 
the shared electrons can be distributed, like the unshared, into 
subgroups of two and six. It is more probable that the arrange- 
ment of the octet is quite different when it consists of shared 

II. If the shared electron really encircles both nuclei, it must 
approach each the same number of times per second. Hence the 
periods of rotation of the subgroups in each atom of which it 
forms part must agree. 1 Moreover, in a chain of covalently 
linked atoms this must be true of any two neighbours, and so of 
the whole chain. It is of course possible that the subgroup which 
the shared electrons enter is not the same in each atom, and so 
the periods need not be identical, but they must be rationally 
related to one another. This suggests a way in which an atom 
in one part of a molecule may influence all the others, and also 
gives a condition for the stability of a molecule which may 
ultimately prove of great importance. 

III. In some discussions on covalency it has been pointed out 
(for example, by Fowler, Sommerfeld, and others) that the 
hydrogen ion occupies a peculiar position from its small size. 
So we may suppose that carbon, nitrogen, oxygen, and fluorine 
complete their octets by taking up 4, 3, 2, and 1 atom of hydro- 
gen respectively : these provide the lacking electrons, and the 
protons slip into the electron loops, so to speak, without much 
affecting the structure. This way of regarding the process may 
be quite sound ; but any physical theory founded on it must 
take account of the fact that whatever a hydrogen atom can do 
in this way a hydrocarbon radical like ethyl or even phenyl can 

1 See Wilsdon, Phil. Mag. 1925, 49, 864, 900. 

102 Covalent Links 

do likewise. There are of course plenty of differences between 
the behaviour of a hydrogen atom and that of an alkyl group ; 
but from the covalency point of view they are equivalent, and 
a theory of the sharing of electrons must not be made to depend 
on the small size of the hydrogen ' core ', but must be equally 
applicable to larger atoms. It is indeed rather remarkable, in 
view of the great physical contrast between the single proton 
which forms the core of the hydrogen atom, and the much larger 
carbon nuclei with their attendant K electrons which the heavier 
groups possess, that we do not find more differences between a 
hydrogen compound and its alkyl substitution products. Certain 
marked differences there are, as in the case of displacement of 
the hydrogen and its power of co-ordination : but the replace- 
ment of one by the other is almost always possible, and it causes 
less alteration of the properties of the molecule than might on 
physical grounds have been expected. One of the few marked 
distinctions would seem to be in the power which hydrogen 
possesses of forming covalent links by means of a single electron. 

One-electron Covalencies. 

While in all ordinary cases the evidence is strongly in favour 
of every covalent link being constituted of two shared electrons, 
there are a small number of compounds in which it is almost 
certain that a single shared electron can form a Imk. The most 
indisputable of these are two forms of hydrogen. The existence 
of neutral H 8 has recently been shown to be very doubtful ; but 
there is no doubt that in positive ray tubes molecules of [H 2 ] + 
and [Hg]+ frequently occur. 1 The first of these has two nuclei 
and only one electron : the second has three nuclei (and so at 
least two links) and only two electrons. In each therefore one 
electron must be able to hold two atoms together. These forms 
have been described as stable, but this only means that they are 
formed in fair quantity in the positive ray tube, and appear to 
persist for the short time that it takes a positive ray to travel 
along the tube. Being charged molecules they cannot of course 
be isolated any more than [H]+ can be isolated ; but if they had 
the stability of an ordinary ion, it should be possible to separate 
them in the form of neutral compounds with an anion, that is, 

1 Aston has shown that the masses of these are 2 016 and 3 024 re- 

One-electron Links 103 

of salts : we ought to be able to obtain [H 2 ]C1 and even [HJC1, 
as we can obtain [H]C1. The fact that such compounds have 
never been obtained is evidence these molecules with one-elec- 
tron links are, on the chemical standard, very unstable. 

The only other group of compounds in which we must admit 
the existence of one-electron links is that of the hydrides of boron. 
There are several of these, all of which agree in containing more 
hydrogen than can be accounted for on the assumption that 
boron is trivalent in the ordinary sense. They have been very 
carefully investigated by Stock, and there is no doubt about their 
composition and molecular weight. We may take the simplest 
as an example. This is B 2 H 6 , a gas boiling at almost exactly the 
same temperature as ethane. With trivalent boron we should 
expect B 2 H 4 . The molecule must have seven links, one between 
the boron atoms and six to the six hydrogens. Apart from the 
two K electrons of the boron (the utilization of which for co- 
valency formation would involve an impossibly great expendi- 
ture of energy), there are twelve available electrons, six from the 
hydrogens and three from each boron. It is impossible to 
account for this except by supposing that two of the hydrogen 
atoms are attached by one electron each. These compounds are 
also unstable : they are decomposed by water, they are im- 
mensely powerful reducing agents, and they all give off hydrogen 
either in the cold or on gentle warming. 

In addition to their instability all these compounds have this 
point in common that one of the atoms attached by a single 
electron is always hydrogen. That this is not an accident is 
shown by comparing the hydrides with the other compounds of 
boron. The halides and the alkyl derivatives are all of the 
type BX 3 , and careful investigation by Stock has shown that 
they give no sign of association to BgX 6 down to the lowest 
temperatures, while the hydride has no tendency to dissociate 
into BH 3 up to the temperature at which it begins to decompose 
with loss of hydrogen. 

We may therefore conclude that the occurrence of links 
formed of a single shared electron is very rare : that such links 
are always unstable : and that they are only possible at all when 
one of the atoms so linked is hydrogen. 1 

1 The possible existence of a link formed of three shared electrons will 
be considered under carbon. 

104 Covalency and the Periodic Table 

Covalency and the Periodic Table. 

The conditions which determine whether an atom tends to 
form ionized or covalent compounds have been discussed by 
Fajans, 1 whose conclusions are simple and convincing, and 
strongly supported by experiment. In an ionized molecule it is 
clear that the electrostatic attraction will bring the ions into 
close contact, and will distort the orbits of the outer electrons. 
If we imagine this attraction to increase, the distortion will 
increase with it, until a point is reached at which the system 
breaks down : the distorted orbits become less stable than orbits 
enclosing both nuclei, and the electrovalency goes over into a 
covalency. The chief factor in determining the change is of 
course the magnitude of the charge, and that is why the ioniza- 
tion ceases when the valency exceeds a certain value. Further 
consideration shows that the orbits whose distortion concerns us 
are those of the negative and not those of the positive ion. These 
contain the electrons which are ultimately to be shared between 
the two atoms, and their stability is weakened by the negative 
charge (and the more so, the larger this is, i.e. the smaller 
the nuclear charge for a given number of electrons), while that 
of the cationic orbits is strengthened by the positive charge on 
the cation. The size of the ions will also be of importance. The - 
smaller the cation is the stronger will be the attraction it exerts 
on the anionic electrons, and the more likely they are to go over : 
while with the anion, an increase of size will weaken the stability 
of its electrons, since they will be further removed from the 
influence of their nucleus. 

We thus arrive at the general conclusions that an electro- 
valency will tend to pass" over into a covalency 

(1) When the charge on the ion is large, whether it is positive 
or negative. 

(2) When the cation is small. 
(8) When the anion is large. 

In applying these conclusions we have to remember that in 
any periodic group the size increases on the whole with the 
atomic number, but that (especially in the earlier groups) the ions 
-4 of the B subgroup are much smaller than those of the A. Hence 
we should expect to find that ionization was in general greatest 
among the elements of lower valency : that with the metals it 

1 Fajans and Joos, Z.f. Phys. 1924, 23, 1 ; Fajans, Naturwiss. 1923, 11, 
165 ; Z.f. Krystallogr. 1925, 61, 18. 

Conductivity of Chlorides 105 

was more marked in the heavier than in the lighter members of 
a group, and more in the A than in the B subgroup : * while 
among the electronegative elements it should be more prevalent 
among the lighter than among the heavier atoms. 

It remains to see how far these principles are confirmed by 
observation. We have several methods for determining the 
tendency of molecules to ionize under various conditions. There 
is the obvious test of iomzation in water, the indications given 
by the volatility, the work of Biltz on the electrical conductivity 
of the pure fused chlorides, and the results of Grimm and Som- 
merfeld, based on the crystalline structures. 

Biltz 2 collected the data as to the conductivities of a large 
number of pure chlorides just above their melting-points, most 
of which he had measured himself. The results are complicated 
by the fact that they have to be measured over a very wide range 
of temperature, since the compounds must be in the liquid state. 
The conductivity always increases with the temperature, but to 
very varying extents ; and, except that the temperature co- 
efficient is greater the smaller the absolute conductivity, we do 
not know what this correction amounts to, and so we cannot 
make allowance for it. We must take the results as they stand, 
as depending both on the tendency of the compound to ionize, 
and on the height of its melting-point. Since the melting-points 
of ionized compounds are always higher than those of covalent 
compounds, this has the result of exaggerating the natural differ- 
ences in conductivity, and dividing the compounds very sharply 
into two classes ; but the conductivities vary over so large a 
range (m the ratio 1 : 10 s ) that the temperature effect is m com- 
parison almost negligible. Out of 60 chlorides of 58 elements 
examined 31 were found to have conductivities lying between 
10 and 1 (ohm" 1 cm. at the melting-point) while for 26 the 
value was less than 2 x 10~ 8 . Only 3 came within these wide 
limits : BeCl 2 , 0032 at 451, ZnCl 2 , 8 x 10~* at 318, and 
HgCl a , 0-8xlO- 4 at277. 8 

The work of Grimm and Sommerfeld 4 has already been men- 
tioned. They deal only with compounds of the general formula 

1 There is evidence that apart from the difference m size cations of 
inert gas numbers have more effect than others in deforming anionic 

2 Z. anoTg. Chem. 1924, 133, 312 ; Biltz and Klemm, ibid. 1926, 152, 267. 
s HgBr 2 (0 0015 at 235), HgI 2 (0 012 at 252), and InI 3 (0 054 at 210) 

have similar intermediate values. 4 Z.f. Phys. 1926, 86, 36. 

3 o6s p 

106 Covalency and the Periodic Table 

AB, in which therefore if A is from the Nth periodic group, 
B is from the (8 - N)th (IV, IV : III, V : II, VI : I, VII), and 
regard them as ionized when they have either a rock salt (6:1) 
or caesium chloride (8:1) lattice, and covalent when they have 
a diamond (4 : 1) or wurtzite (4 : 1) lattice. It is uncertain whether 
they are justified in drawmg so absolute a conclusion : various 
objections can be raised to it, especially that some of the ele- 
ments of the fourth group (which they include as being so to 
speak of the AA type of formula) such as tin, crystallize in a 
diamond lattice and yet have a considerable conductivity (at any 
rate in comparison with the almos$ completely insulating dia- 
mond), which would seem to suggest ionization. However, their 
conclusions may be given : they certainly fall into line with the 
rest of the evidence. They involve the assumption, for all com- 
pounds except those of elements of the fourth group, of a trans- 
ference of electrons by a sort of co-ordination. In zinc sulphide 
(wurtzite), for example, we must suppose that the sulphur gives 
up two electrons to the zinc, so that each atom has four, like 
carbon and silicon, enabling the compound to form a giant mole- 
cule of four-covalent atoms like carborundum : the formula of 
the ionized form being [Zn] ++ S , that of the covalent should 
be written (Zn S ++ ) w . The evidence of the intensities of the 
X-ray reflections certainly does not disprove this, though it may 
be doubted whether it is of great value in supporting it. 

The evidence available from these various sources as to the 
tendency of the elements to form ions may be summarized under 
the vanous periodic groups. 

Group I A. (Alkali metals, the largest cations, with the smal- 
lest charge.) Their compounds, such as the hahdes, are 
always ionized under all conditions./ 

Group I B. Cuprous chloride and silver halides are ionized in 
water (so far as they dissolve). The crystal structure of 
cuprous chloride, bromide, and iodide are all of the diamond 
type ; silver iodide crystallizes both in the diamond and in 
the wurtzite forms, but the bromide and chloride in the 
sodium chloride %rm. Here the much smaller cations have 
a stronger tendency to form covalencies, and this is more 
marked in copper, because it is the smaller of the two. In 
the fused state, however, both cuprous and silver chlorides 
are ionized. 

Group II A. The salts of the typical and A elements are all 
ionized in water : all the chlorides are good conductors 

Covalency and the Periodic Groups 107 

except that of beryllium. Magnesium oxide and the sul- 
phides of magnesium, calcium, strontium, and barium ate 
all of the rock salt type. But beryllium, which is much the 
smallest, gives an oxide of the wurtzite type, and its chloride 
is a poor conductor. 

Group II B. These elements all show a very limited power of 
ionization. Cadmium chloride is imperfectly ionized in 
water, and mercuric chloride is definitely a weak electrolyte. 
Of the fused salts also the conductivities are low, and that of 
mercuric chloride very low (the tendency of mercury to 
assume the covalent form is quite exceptional, and must be 
due in part to causes outside the Fajans theory). Zinc oxide 
(but not cadmium oxide) and the sulphides of all three 
metals have covalent lattices. 

Group III A. Boron shows no signs, of ionization by any test. 
Aluminium chloride is ionized in water, but not in the fused 
state, as the volatility and absence of conductivity show. 
Its nitride A1N has the wurtzite structure. Scandium 
chloride is ionized in water and in the fused state, and its 
nitride ScN has the rock-salt structure. Yttrium and lan- 
thanum chlorides are good conductors when fused. The 
progress of ionization with increase in atomic number is very 
marked in this group. 

Group III B. The chlorides of all these elements, so far as they 
can be measured, are good conductors when liquid : GaCl 3 , 
InCl 3 , InCl a , InCl, T1C1 ; T1C1 3 appears to decompose when 

Group IV : typical and B elements. All their chlorides of the \ 
type XC1 4 (C, Si, Ge, Sn, Pb) are non-conductors in the ] 
liquid state, exeep^'-ThGi^. 

Group IV A. TiCl 4 is a non-conductor in the pure state : the 
other chlorides cannot be measured. The carbides of tita- 
nium and zirconium are, however, of the rock salt type. 

Grimm and Sommerfeld have included in their investiga- 
tion the free elements of the fourth group, which may be 
regarded as 1 : 1 compounds of the element with itself. They 
find that all the typical and B elements with the exception 
of lead, whose structure is imperfectly known, have the 
diamond structure, but that all the A elements (Ti, Zr, Ce, 
Hf, Th) have a close-packed structure. 

This concludes the list of elements which can form cations, ' ' 
and it will be seen that the theory of Fajans is entirely confirmed. 


Covalency and the Periodic Table 

The same is true of the formation of anions, though the evidence 
is less full, since we are concerned only with the halogens and the 
oxygen-sulphur group. Here, according to Fajans, we ought to 
find that size has the opposite effect : the smallest and lightest 
atoms should show the greatest tendency to ionize. 

We have already seen that the boiling-points indicate that 
with certain elements the fluorides are ionized while the other 
halides are not. This difference is very marked with the com- 
pounds HgX 2 , AlXg, and SnX 4 , and indications of it arc found 
with ZnX 2J CdX 2 , SbX 8 , TiX 4 , GeX 4 (X- halogen). The 
crystallographic data confirm this conclusion. Silver iodide 
has a diamond and wurtzite lattice (in the two forms) while 
the fluoride, chloride, and bromide all have ionic lattices. In the 
same way among the elements of Group VI cadmium oxide has 
an ionic and cadmium sulphide a covalent lattice. 



WE have adopted the term ' co-ordinate ' to describe those 
covalencies in which both of the shared electrons are derived 
from the same atom, since it is the recognition of this form of 
linkage which makes it possible to reconcile the theory of co- 
ordination, by which Werner was able to throw so much light 
on the behaviour of inorganic compounds with that of structural 
chemistry. We may therefore briefly consider the new ideas of 
molecular structure which Werner introduced, and the way in 
which the electronic theory is able to interpret them. 

Werner's Theory of Co-ordination 

This theory, which was first suggested in 1891, and developed 
more fully in 1893, 1 originated in an attempt to explain the 
structure of a series of so-called ' molecular ' or ' complex ' com- 
pounds formed by the combination of apparently saturated ^ 
molecules, and especially of those which many salts form with 
ammonia. The attempts which had been made to give structural 
formulae to these (often very stable) compounds were admittedly 
unsatisfactory. Werner proposed an entirely new principle of 
molecular structure : that it was (at least largely) determined 
by the tendency of certain atoms to attach to themselves a 
definite number of other atoms or groups, irrespective of whether 
these were univalent atoms or groups, or whole molecules capable 
of independent existence. This number he called the ' co- 
ordination number ' : every atom had a maximum co-ordination 
number, usually six or (less often) four, although it could also 
form ' co-ordinatively unsaturated ' molecules, in which this 
number was not reached. In addition to the atoms or groups 
of this co-ordination complex, which were said to occupy the 
' first sphere ', the molecule might contain other atoms or groups 
less closely attached in a ' second sphere ' : these did not count 

1 Alfred Werner, ' Beitrage zur Theorie der Affimtat und Valenz ',1891 . 
Z. /. anorg. Chem. 1898, 8, 267. This latter paper contains the essential 
principles of the theory, which were not seriously altered, although they 
were very greatly developed, in his ' Neuere Anschauungen auf dem 
Gebiete der anorganischen Chemie ', of which the first edition appeared m 
1905, and the last in his lifetime (he died in 1919) in 1913. 

110 Co-ordination 

towards the co-ordination number. For example, in the hcxa- 
mine of cobaltic chloride [Co(NH 3 ) e ]Cl 3 the ammonia molecules 
were regarded as occupying the first sphere of the cobalt and 
satisfying its maximum co-ordination number 6, while the 
chlorine atoms occupied the second sphere. Experimentally the 
groups in the outer sphere were characterized by being ionized 
in water, while those constituting the co-ordination group wore 
not. To mark this distinction Werner introduced the square 
bracket [ ] to enclose the atoms which formed the co-ordination 
complex and were not ionized. This symbol was an essential 
part of the theory, and he was careful to justify the position lie 
assigned to it by experimental determination of the degree and 
nature of the ionization. To allow of the attachment to the 
central atom of more groups than the ordinary valency per- 
mitted, Werner adopted the idea of subsidiary valencies, indi- 
cated by dotted lines to distinguish them from the ordinary 
valencies ; this part of the theory however need not detain us': 
it was ultimately admitted, if not by Werner at least by his 
successors, that within the co-ordination group when once it was 
constituted, this distinction vanished, and all the valencies 
attaching the groups to the central atom were identical. 

Werner assigned definite positions in space to the groups in 
a co-ordination complex.* Where there were 4, an arrangement 
at the points of a tetrahedron had already been established for 
carbon by van t Hoff ; but Werner showed that a different 
arrangement must occur in the 4-co-ordinated compounds of 
platinum: these are never optically active, but those of the 
type Fta b. occur m two (geometrically) isomeric forms, which 
6 f Urrou P s are * ** ^me plane with the 

atom, but not if they^oecupy the qorners of a tetrahedron 
U a 6 - c - rd inated complex he assigned the 

o, 3JS 

For further details see Chapter XII. 

Werner's Theory 111 

compare the formulae of any particular series of compounds such 
as those formed by the combination of platinic chloride with 
ammonia. In the following list the position of the square 
brackets has in every case been determined by experiment. 
Under each formula is given the molecular conductivity at 25 
and V =1000 : this is roughly proportional to the number of 
ions into which the molecule dissociates in solution : 

[Pt(NH 3 ) 6 ]Cl 4 [Pt(NH 3 ) 5 Cl]Cl 3 [Pt(NH 3 ) 4 Cl 2 ]Cl a 

523 404 220 

[Pt(NH 3 ) 3 Cl 3 ]Cl [Pt(NH 3 ) 2 Cl 4 ] [Pt(NH 3 )Cl 5 ]K 

97 108-5 



The co-ordination number is 6 throughout : the platinum 
atom always has six groups (NH 3 or Cl) attached to it by non- 
ionized links. But there is the further remarkable fact that 
whenever a whole molecule of ammonia is replaced within the 
complex by a univalent group (Cl), the complex loses one positive 
charge, its electrovalency falling by one if it is positive, and 
rising by one if it is negative. 

Platinous chloride gives a similar series of ammines, but in 
these the co-ordination number is four. They behave in exactly 
the same way : 

[Pt(NH 3 ) 4 ]Cl 2 [Pt(NH 3 ) 3 Cl]Cl [Pt(NH 3 ) 2 Cl 2 ] 

260 116 

[Pt(NH 3 )Cl 3 ]K [PtClJK, 

107 267 

This characteristic change of electrovalency is universal in all 
these series of compounds, whether the central atom is platinum, 
cobalt, chromium, or another metal : and whether the attached 
groups are on the one hand ammonia, water, or other molecules, 
or on the other hand chlorine, bromine, N0 2 , or other univalent 

The fundamental points in Werner's theory thus are (i) the 
importance of each central atom being attached by non-ionized 
links to a definite number usually six, less often four of other 
atoms or groups, this number having no relation to the periodic 
group of the central atom ; (u) the fact that these groups may 

112 Co-ordination 


either be univalent atoms or radicals, or whole molecules ; and 

'(iii) the universal change in the electrovalency of the compound 
when a group belonging to one of these types is replaced within 
the complex by one of the other type. 

Werner maintained that the undeniable successes of the theory 
of structural chemistry in dealing with organic compounds were 
due to its being, in the special case of carbon, in many ways 
identical with the co-ordination theory, because carbon was in 
the unique position of having a valency identical with its maxi- 
mum (and usual) co-ordination number a remark which, as we 
shall see, goes far to explain the exceptional position of carbon. 
To the ordinary chemist it appeared that Werner had not 
succeeded in dethroning structural chemistry so far as organic 
compounds were concerned, but that he had provided a new 
theory of structure which was of great value in accounting for 
the behaviour of inorganic compounds, especially of those com- 
plex or ' molecular ' compounds with which the old structural 
theory had proved itself incompetent to deal. 

This was clearly an unsatisfactory position ; it represented 
molecules as being built on two different and apparently irre- 
concilable plans, and it emphasized an obviously false distinction 
between organic and inorganic chemistry. The conflict could 
only be temporary : it must ultimately be resolved by the dis- 
covery of a more complete theory of valency, of which the struc- 
tural theory and the co-ordination theory would prove to be 
partial aspects. The solution was provided by the electronic 
theory, with the recognition of the third type of linkage, a 
covalency in which both electrons are supplied by the same atom. 

Electronic Interpretation of Co-ordination 1 

In the first place it is clear that the links which join the units 
of a co-ordination complex to the central atom are covalent. 
This is really self-evident if our theory is true, since Werner 
showed that they were not ionized, and a covalent link is the 
only alternative which we have admitted ; but it is established 
conclusively by the final tests of geometrical and optical iso- 
merism. Hence the maximum co-ordination number is the 
maximum covalency number: an atom with a co-ordination num- 
ber of six is one which can form six covalencies, and so can have 
a valency group of twelve shared electrons. We have already 

1 See Sidgwick, J. C. S. 1923, 123, 725. 

Electronic Interpretation 113 

seen that this is possible, and that it occurs in such compounds 
as SF 6 and K 2 [SiF 6 ]. Similarly a co-ordination number of four 
implies a valency group of eight, which of course is the most 
familial 1 form. So far there is nothing involved in the co-ordina- 
tion theory which we have not already accepted. The attach- 
ment of a univalent radical like chlorine or NO 2 is a covalency 
of the normal type, to which the radical in question supplies one 
electron, and the central atom the other. But an independent 
molecule like water or ammonia must already have an even 
number of valency electrons, and so cannot form its linkage in 
this way : if it had a single odd electron available for the pur- 
pose, or if it could accommodate one further electron borrowed 
from the central atom, it would not be able to exist by itself ; 
it must attach itself by sharing with the central atom a lone pair 
of its own electrons in other words, by forming a co-ordinate 
link. All the molecules capable of entering into a complex in 
this way can be shown to have the necessary lone pair : the 
nitrogen in ammonia has one such pair, and the oxygen in water 
has two. Thus the number of shared electrons in the valency 
group of the central atom will be the same whether the co- 
ordinated units are molecules or univalent radicals, and thisi 
explains why those of one kind can replace those of the other ) 
unit by unit, as they are found to do. 

The characteristic change of electrovalency which accom- 
panies such a replacement necessarily follows. Suppose we start 
with the non-ionized compound [Pt(NH 3 ) 2 Cl 4 ]. If a (neutral) 
chlorine atom is removed, it will take with it one of the electrons 
which it previously shared with the platinum, but will leave the 
other behind. If now an ammonia molecule takes its place, this 
provides the two electrons required for its attachment, so that 
the platinum has gained one electron by the exchange. Since it 
must in the original compound have had the number of electrons 
required for stability, it now has one too many : it will lose this, 
and thereby acquire a positive charge, appearing as a cation in 
the salt [Pt(NH 3 ) 3 Cl s ]Cl. The process can be represented by 
the scheme : 

[Pt*Cl] > [Pt x ] [Pt:NH 3 ] > [Pt:NH 3 ] + 


This change of electrovalency on replacement is not peculiar 
to the Wernerian complexes. There is a very familiar example 
in organic chemistry, though it is not usually formulated in this 
way. When ammonia acts on methyl chloride, methylamine 


hydrochloride is formed : the chlorine is replaced by NH 3 , and 
the electrovalency of the complex changes from zero to +1 : 1 

" HH 


+ NH 3 


NH 3 


This suggests another way in which the reaction may equally 
well be described. The nitrogen of the NH 8 in the complex is 
quadrivalent : it is in the form of a substituted ammonium, with 
all the rest of the complex as substituent. In order to become 
quadrivalent nitrogen must, as we know, lose an electron. Hence 
we may say that a neutral chlorine atom is first removed from 
the central atom ; the ammonia molecule then gives up an 
electron to the chlorine, converting it into chlorine ion, and the 
resulting positively charged univalent radical [ -NH 3 ] + takes 
the place of the chlorine, carrying its positive charge into the 

The position is perhaps made clearer (and the formulae are 
certainly easier to remember) if we consider how many electrons 
the central atom has gained or lost by forming the complex. 
Every molecule (as NH 3 ) added gives it two : every univalent 
radical gives it one : further, the electrovalency of the complex 
must be added if it is negative, and subtracted if it is positive. 
Thus we have 

[PtCl e ]~~ +6 + 2 =8 

[Pt(NH 3 )Cl 5 ]- +2+5+1 =8 
[Pt(NH 3 ) a ] ++++ +2x6-4 =8 

It will be seen that all the 6-co-ordinated platinum compound.' 
whose formulae are given on p. Ill show in this way a gain o 
eight electrons. Similarly the 4-co-ordinated compounds o 
platinum all show, like [Pt(NH 3 ) 4 ]Cl a (2x4-2 = 6), a gam o 
six. These numbers, which may perhaps be called the ' cffcctivi 
valencies ' of the central atom, arc characteristic for each par 
ticular series of compounds : thus for the ammines of tnvalcn 
cobalt and chromium the number is nine, as in [Co(NH 3 ) ]Cl 

Werner's theory was not limited to the peculiar addition com 
pounds which we have been considering, and with which hi 
name is especially connected. He applied it in great detail t 

1 Ramsay gave a very similar explanation of this reaction in 100 
(J. C. S. 93, 785). 

Electronic Interpretation 115 

the whole of chemistry more particularly inorganic chemistry 
and throughout his applications it is found that the electronic 
interpretation of his theory holds good. It is thus clear that 
there is no real opposition between the Werner theory and that 
of structural chemistry. The same electronic principles can be 
applied to both : they are different aspects of the same process, 
the former recognizing the existence of these peculiar co-ordi- 
nated compounds which the latter, in its classical form, dis- 
regards ; and the reason why the structural theory, in spite of 
disregarding them, has been of so much service in organic 
chemistry is very largely that suggested by Werner, that carbon, 
having the number of valency electrons required to give it 
directly its maximum covalency of four, seldom if ever forms, 
co-ordinate links. Other elements often do so, and hence struc- 
tural chemistry could not deal with them satisfactorily until it 
had taken co-ordination into account. 

This interpretation breaks down the supposed distinction be- 
tween organic and inorganic chemistry which the opposition of 
these two theories had suggested. It also removes an apparent 
weakness in the Werner theory, that it seemed to attribute a 
unique character to one atom in the molecule, as the ' centre of/ 
co-ordination ' . It is now evident that this is merely an arbitrary 
distinction, a matter of convenience. Every atom hi the mole- 
cule is a centre in the same sense, though some will have a higher 
co-ordination or covalency number than others. Every atom has 
a valency group of electrons made up by the same processes to a 
stable number, and the molecule owes its existence to this stability. 

There are many sides of Werner's theory which have not yet 
been touched upon. One of the most valuable is the funda- 
mental importance which he ascribes to the co-ordination num- 
ber, that is, as we now understand it, to the number of shared 
electrons ; this is in complete agreement with the electronic 
theory, but could scarcely have been deduced from it ; and in 
recognizing its importance, Werner undoubtedly made a great 
advance in our knowledge of the principles of molecular struc- 
ture. This question, together with the equally important one of 
the relation between this number and the structure of the atom, 
will be more fully discussed in Chapter IX. Other aspects of the 
theory will naturally arise later. Any discussion of molecular 
structure involves frequent reference to the conclusions of Wer- 
ner, whose insight into such problems was extraordinarily acute. 

116 The Co-ordinate Link 

Conditions of Formation of Co-ordinate Links 

When a co-ordinate link is formed between two atoms, one o 
them gives the other a share in two of its own (previously un 
shared) electrons : 

A + :B * A:B (A--B). 

It is therefore of the essence of this type of link that, unlike j 
normal covalency, it requires for its formation two atoms o 
different characters : this distinction, which was not apparen 
in Werner's theory, is of fundamental importance. In order t< 
express these two functions, we may call the atom which lend, 
the two electrons (A above) the donor, and the one which receive, 
them (B) the acceptor. A necessary condition for the donor i, 
that it should possess a loneTpair "of valency electrons : a ' co 
valently saturated ' molecule like CH 4 or C 6 H 12 cannot pro 
vide a donor, because all its valency electrons are already shared 
This condition is of course not sufficient (an atom which ha, 
a lone pair may refuse to act as a donor), because the produc 
may be unstable ; but the same may be said of any of th< 
general conditions of chemical combination. In forming th< 
link, the donor does not change the number of its valency elec 
trons, while the acceptor increases its own number by two 
Hence if the valency group of the donor is of a stable size af te 
co-ordination, it must have been so before : the donor mus 
have formed part of a stable molecule. This was the funda 
mental problem which Werner had to solve, that molecule, 
apparently saturated still had the power of further combination 
The acceptor, on the other hand, must have room in its valency 
group for two more electrons. This may arise in four difleren 

(1) The acceptor may be a truly unsaturated isolated divalen 
atom, as of oxygen or sulphur, having only six valency electron, 
to start with : 

(C 2 H 6 ) 3 N + O (C 2 H 5 ) 3 N->0. 

In such compounds the co-ordinate link is exceptionally strong 
because if it breaks the acceptor fragment is highly unstable 
Links of this kind always appeared in the older formulae a: 
double bonds as in (C 2 H 5 ) 3 N=0. 

(2) It may have an incomplete ' octet ' of shared electrons 
as in Mg(CH 3 )I, where the magnesium has four, or in BC1 3 
where the boron has six shared electrons : such imperfect valency 

Conditions of Formation 117 

groups, when they are all shared, are not too unstable for 
molecule to exist. Examples of the products of co-ordination of 
such atoms are the compound of boron trichloride and ammonia 
H 3 N->BC1 3 , and the Grignard reagent : 

(C 2 H 6 ) 2 (K 

(C 2 H 5 ) 2 X 

(8) A stable cation like Na + or Zn ++ , although it has a com- 
plete (unshared) outer group (which may or may not be called 
a valency group) of eight or eighteen electrons, can take up 
another complete and wholly shared valency group of eight or 
more. The positive charge on the cation will promote the co- 
ordination, as it increases the tendency to borrow negative 
electrons. The factors indicated by Fajans as assisting the 
formation of covalencies the influence of the magnitude of the 
charge and the size of the ion will of course be important in 
such a case. (It may be pointed out that the elements which 
form particularly stable ammines, such as the transition ele-1] 
ments, have a very small atomic volume, as Fajans' theory r 
requires.) It is this process which leads to the hydration of ions 
in solution, and in the solid salt. 

(4) Since the octet is not the only form of stable group, but 
can expand with some atoms to twelve or even sixteen electrons, 
an atom with a completed octet may act as an acceptor by in- 
creasing its valency group. Thus we have the reaction 

SiF 4 *K 2 [SiF 6 ], 

where the silicon forms links in this way with two fluorine ions, 
its octet expanding to twelve. 

Under this head must be included hydrogen, of which the 
valency group is normally two, but can, as we have seen, be 
increased by co-ordination to four. The question of the con- 
ditions which make such an increase possible (either with hydro- 
gen or with other atoms) is of great interest, but as yet no 
general answer can be given to it. With hydrogen, co-ordination 
only occurs readily if it is in a hydroxyl group (water, alcohols, 
phenols, acids), or is attached to fluorine (in H 2 F 2 ) ; when the 
hydrogen is attached to nitrogen, as in the amines, it can occur, 
but much less easily ; with hydrogen attached to carbon it is 
almost unknown. 

These are the general conditions of formation of co-ordinate 
links. There are two classes of co-ordinated compounds which 

lib The Co-ordinate Link 

are of special importance and may be mentioned here, double 
salts and chelate compounds (the still more important class of 
associated substances is discussed in the next chapter). 

Double Salts 

It cannot always be assumed that a ' double salt ' a solid 
phase whose composition can be expressed as the sum of an 
integral number of simple salt molecules of more than one kind 
(with or without solvent molecules) really contains a complex 
molecule; there is always a possibility that it is only a crystalline 
aggregate of simple salt molecules. It is an experimental ques- 
tion, which in general can only be decided by determining 
whether the complex exists in solution, although in some cases 
the X-ray evidence of crystal structure may be sufficient. Proof 
that dissociation into the components occurs in solution is not 
decisive against the existence of the complex, unless the dis- 
sociation can be shown to be complete : many true complex 
salts, like the fluosilicates, are considerably dissociated in this 
way. Where however the complex exists, the mechanism of 
its formation is simple. Suppose we start with salt MX m (X = 
univalent radical). In the non-ionized form the metal M is 
exerting m covalencies. If this forms a complex salt with n 
molecules of, say, an alkaline salt BX, the M atom, (as acceptor) 
forms co-ordinate links with n more X ions : this gives it n 
negative charges, which are neutralized in the separated salt 
by n B + ions, giving the complex salt B n [MX^J, in which the 
atom M has a covalency of m + n. Thus mercury in the covalent 
form of mercuric iodide I Hg I has a valency group of four 
shared electrons, two from the mercury and one from each of 
the iodine atoms. In presence of potassium iodide it can co- 
ordinate with another iodine : this was originally an ion, with 
its octet completed by the transference of an electron from a 
potassium atom : it lends two electrons to the mercury, which 
becomes 8-covalent, and the complex has the negative charge 
due to the iodine ion : this gives K[HgI 3 ]. The same process 
can occur again, giving a complex with two negative charges 
and a 4-covalent mercury atom, in K 2 [HgI 4 ]. The reaction 
may equally well be represented by saying that the mercury 
acquires the two electrons necessary for its new covalency, one 
from the potassium and the other from the (neutral) iodine. The 
formula of the resulting salt must always be the sum of those 
of a few molecules of the components. As we have seen, it is 

Double Salts 119 

idle to ask whether the linkage of the X groups to the central 
atom is normal or co-ordinate. If we imagine the reaction to 
be directly between the mercuric iodide and an iodine ion we 
should call it co-ordinate : if the potassium is supposed to 
transfer an electron to the mercury, and so make it trivalent 
and capable of combining with another (neutral) iodine atom, we 
should call it normal. But if we wish to call the link co-ordinate 
we must not write it Hg-<-I, which would imply that a neutral 
iodine atom with seven valency electrons had lent a pair to the 
mercury, but Hg<-[I]~, since it is only an ion which could 
form the linkage by co-ordination. If the latter formula means 
anything that [Hg 1]~ does not, it implies that the whole of 
the negative charge resides on the iodine atom, an assumption 
for which there is no justification. In the complex there is no 
difference between the linkage of the first two iodine atoms of 
the HgI 2 and that of the others : the molecule, if it is to be 
written in full, is 

It has however this in common with other co-ordinated com- 
pounds, that it can break up comparatively easily into its 
components potassium iodide and mercuric iodide, since these 
are both stable molecules. 

Chelate Compounds 

In the compounds we have so far discussed, the donor and 
acceptor originally formed part of two separate molecules. It 
is however equally possible for co-ordination to take place be- 
tween two atoms which already form part of the same molecule. 
In that case the product must contain a ring, and such substances 
have been called by Morgan by the convenient name of ' chelate ' 
compounds. 1 Their existence was for a long time unrecognized, 

1 From xn^i a cr& b' s claw (Morgan and Drew, J. C. S. 1920, 117, 1457, 
note). Professor Morgan applies this term to all rings containing co- 
ordinate links, and so includes, for example, Werner's ethylene diamine 
(en) compounds, with the ring 



From our point of view, those with only one such link in the ring are of 
more interest. 

120 Co-ordination Compounds 

since the molecule could be represented as an open chain without 
assuming a co-ordinate link : the discovery of their nature was 
due to Werner. They are a peculiarly stable group of com- 
pounds, probably because the normal covalencies hold the mole- 
cule together even if the co-ordinate link breaks. The most 
remarkable are the metallic derivatives of the /8-diketones, and 
especially of acetylacetone. These diketones are definitely 
though not strongly acidic, and evidently react in the enolic 

CH a -C=CH-C-CH 8 

form, as I II This substance, acetylacetone, 

OH O y 

forms compounds with a surprisingly large number of elements 
(over sixty), in which an atom of the element replaces the 
hydroxylic hydrogen in one or more molecules of the ketone, 
according to the ordinary rules of valency. Thus if we write A 
for the radical C 5 H 7 O a remaining when this hydrogen is removed, 
we have such compounds as NaA, BeA 2 , A1A 8 , ZrA 4 . These 
were originally (and naturally) assumed to be salts. A few, such 
as those of the alkali metals, actually are salts and behave as 
such, but the majority have quite different properties. They 
have low melting-points and are volatile, sometimes without 
decomposition at atmospheric pressure : they dissolve readily in 
hydrocarbons, and only slightly in water, in which they give 
non-conducting and non-hydrolyzed solutions. All these pro- 
perties show that the compounds are not ionized but covalent. 
The formation of these derivatives is common to /J-diketones m 
general (and to many j8-keto-esters as well), but it does not occur 
with a- or y-diketones : the position of the second oxygen atom 
evidently determines the formation. Werner pointed out that 
this could be explained by supposing that the metal formed a 
co-ordinate link with this second oxygen, with the production of 
a ring. Thus we should write the beryllium compound of acetyl- 

CH 3 

The metal is not ionized. It has a fully shared octet, two of its 
covalencies being normal, and the other two co-ordinate. This 
explains the peculiar non-polar character of these compounds, 
which led to the detection of their structure. 1 

1 The properties of chelate compounds are considered in more detail in 
Chapters IX and XIII. 

Properties 121 

Properties of the Co-ordinate Link 

The peculiar properties conferred on a molecule by the pre- 
sence of a co-ordinate link depend on two characteristics : (1) that 
this link is in general more easily broken than an ordinary 
covalency ; and (2) that it involves an electrostatic disturbance 
in the molecule, and consequently a stronger external field. The 
weakness of this link, which is shown by the ease with which 
an addition compound often breaks up again into its component 
molecules, has led to the belief that it is due to an affinity of an 
inferior order to that of ordinary ' valency ' links possibly to 
an attraction between whole molecules much weaker than that 
which holds together the atoms in each molecule. Even after 
Werner had recognized that the forces were always from atom 
to atom and not from molecule to molecule, the use of such 
terms as subsidiary valency or residual affinity seemed to coun- 
tenance the idea that these links were somehow not quite 
genuine valencies. If we are to maintain that the mechanism 
of a co-ordinate link is the same as that of a normal covalency, 
some explanation must be given of the undoubted fact that it is 
usually easier to break. The explanation is simple. The work 
required to break a link that is, to separate a molecule into 
two parts is the difference between the energy-content of the 
molecule and that of these parts. Hence the more unstable the 
resulting fragments, the more difficult the link is to break. Now, 
as we have seen, it is characteristic of the great majority of co- 
ordinate links that they are formed between atoms previously 
belonging to more or less saturated molecules. The complex can 
therefore break up again into these two molecules, the loaned 
pair of electrons returning to its former place ; and for this 
rupture comparatively little energy is required. But the normal 
covalency cannot do this. If it breaks, it forms two unsaturated 
univalent radicals (' odd molecules ') which are very unstable, 
that is, have a high energy-content. It tends therefore to be 
more stable. It is indeed possible for a normal covalency to 
break in another way without giving ' odd molecules ' : instead 
of one of the two shared electrons going away with each half, 
they may both go with one. In that case the products are ions : 

H;CI: > [HJ+ 

The recombination of ions to form a covalent molecule is in 
fact a kind of co-ordination. But it is only under particular 

3 o6s R 

122 Co-ordination Compounds 

conditions that the parts of a molecule can exist as ions ; and 
when these occur the covalency is of course easily broken. 

This view of the cause of the weakness of co-ordinate links in 
general is confirmed by the fact that one type of co-ordinate link 
is not weak, that in which a neutral divalent atom with a valency 
sextet acts as acceptor (type (1), p. 116). In the amme-oxides, 
or such compounds as sulphuric acid, the co-ordinate link to the 
oxygen is as stable as a normal covalency, the reason being that 
the product of its rupture, an isolated oxygen atom, would be 
as unstable as an ordinary univalent radical. The weakness of 

o-ordinate links in general is therefore a necessary consequence 

if the conditions of their formation. 

It is evident that some disturbance of electrostatic balance 
must accompany the formation of a co-ordinate link. If the 
two molecules between whose atoms the link is formed were 
originally neutral, the acceptor must receive a certain amount 
of negative charge, since it gains a share in two new electrons, 
and the donor must receive an equal positive charge. If we 
assume that the electrons are shared equally between the two 
atoms, each will count as a half for each atom ; the acceptor 
will receive a charge of 1 unit, and the donor of +1 unit. But 
this implies that the electron spends an equal amount of time 
with each of the two atoms, which it cannot be assumed always 
to do. There must in fact be some electrostatic disturbance even 
in a normal covalency (unless the two atoms are the same, as 
in H H or Cl Cl), and this must be subtracted from (or added 
to) the primary disturbance of one unit caused by a co-ordi- 
nate link. Every atom, even that of a monatomic gas like 
argon, has a certain external field ; it is this which gives rise to 
the factor a in the van der Waals equation, and which deter- 
mines the volatility. If there were no such field liquefaction 
would be impossible : if it were constant in intensity we should 
expect that compounds of the same molecular weight would boil 
at the same temperature. But we find that this is not so, and 
that the molecules of compounds even the least ' polar ' 
show signs of a stronger external field than those of elements. 
Argon (mol. wt. 40) boils at -186 C., and oxygen (32) at -183, 
whilst ethane (30) and even methane (16) have higher boiling- 
points of 88 and 161. Hence a compound molecule has 
an increased external field, owing no doubt to the unequal dis- 
tribution of the Unking electrons between the dissimilar atoms 
which share them. The primary assumption that the donor in 

Volatility 123 

a co-ordinated molecule has a charge of +1 unit is therefore 
subject to an uncertain correction. But this correction is evi- 
dently small, and the external field must be much increased by 
the presence of co-ordinate links. This conclusion is supported 
by the properties of substances containing these links, and 
especially by their diminished volatility and then* increased 
dielectric constant. 

(1) Volatility. As we have seen, the large external field of 
ionized molecules diminishes the volatility by holding the mole- 
cules together. A similar but smaller effect is to be expected 
with co-ordinated molecules. The best test of this is to compare 
isomeric compounds, of which one contains a co-ordinate link 
and the other does not. The number of available instances is 
small (in order to avoid possible complications associated liquids 
are excluded), but it is sufficient for our purpose. A good 

example is given by the nitro-compounds R N<d~ and the 
nitrous esters R O N=O. 


Formula. Nitro-compound. Nitrite. Difference. 

CH 3 NO 2 101 -12 113 

C 2 H 5 NO 2 114 +17 97 

C 4 H 9 N0 2 152 75 77 

The difference caused by the co-ordinate link naturally diminishes 
as the molecule grows larger. The aromatic nitro-compounds 
have similarly high boiling-points ; there are no isomeric 
nitrites with which to compare them, but this is shown by the 
fact that nitrobenzene (mol. wt. 128) boils at 208, while chloro- 
benzene (mol. wt. 112 5) boils at 182, and bromobenzene (157) 
at 155. The diethyl ester of ethyl-phosphonic acid 

C 2 H 6 X X OC 2 H 6 

boils at 198, and the isomeric triethyl phosphite P(OC 2 H 6 ) 3 
42 lower, at 156. The amine oxides show the same peculiarity 
in a marked degree. Trimethylamine oxide (CH 3 ) 3 N--O is 
a solid which decomposes without melting at 180, while the 
isomeric ethyl ether of -methylhydroxylamine CH 3 -NH-0 C 2 H 6 
boils at 65. 

(2) Dielectric Constant. This is a measure of the work done by 
an external electric field in orienting the molecules against the 

A*-* \su-or u/inaiion compounds 

effect of their thermal agitation. Its magnitude therefore de- 
pends on the moment of the molecules as dipoles, that is, as 
containing an excess of positive electricity at one part, and of 
negative at another : it thus measures the extent to which the 
electrostatic balance is displaced. While the value of the di- 
electric constant is for hydrocarbons about 2-8 1 (being less for 
the paraffins than for the benzene series), for ethers about 4, 
and for esters about 7 (all these being free from co-ordinate 
links), we find that for nitromethane it is 39 2 and for nitro- 
benzene 86. A striking example is given by the two forms of 
diethyl sulphite: for the true sulphite (C 2 H 5 O) 2 S--O, with 
one co-ordinate link, the dielectric constant is 16, while for the 
isomeric ethyl ester of ethyl-sulphonic acid 

C 2 H B C 

with two such links, it is 42. 

In these examples also I have avoided quoting any associated 
liquids, as they have peculiarities of their own, and will be dis- 
cussed in the next chapter. 

Molecular Volume : Sugderfs Parachor 

Another property which we should expect to be affected by 
the intermolecular attraction caused by the external field of a 
co-ordinated molecule is the volume. As an electrovalency leads 
to a smaller molecular volume than a normal covalency a similar 
effect should be produced by a co-ordinate link ; but the effect 
would not be large, partly because the electrostatic disturbance 
is smaller, but mainly because the co-ordinated group is still held 
in its position by the shared electrons, and close-packing is 
impossible. Hence the effect could not be discovered without 
an accurate means of calculating the contribution of each atom 
to the molecular volume. Until recently no such means was 
available. The work of Kopp, Traube, and others detected 
certain regularities in molecular volume, but the constitutive 

1 The value depends on the temperature, and on the frequency of the 
electromagnetic waves employed for the measurement ; but these factors 
are of subordinate importance, and do not affect the order of magnitude. 

2 In tetranitromethane C(NO 2 ) 4 it falls to 2 3, which is about the value 
for a hydrocarbon. This must be due not to the absence of co-ordinate 
links (of which there is one in each nitro-group), but to their symmetrical 
distribution in the molecule. 

Dielectric Constant : Parachor 125 

element was so large and uncertain that no very detailed con- 
clusions could be based on the results. Even the conditions of ' 
measurement were not agreed upon : Kopp measured his mole- 
cular volumes at the boiling-point, and Traube at a fixed tem- 
perature ; and in neither way were the substances in strictly 
comparable states. The question has been put on a firmer basis 
by the work of Sugden. 1 He pointed out that in calculating the 
molecular volume allowance should be made for the effect of 
the very large internal pressure of liquids, which is manifested 
in the surface tension,/ It has been shown that for a jion- 
associated liquid the influence of temperature on the surface 

" v* 

tension is given by the expression = constant, where y is 

the surface tension, and D the density of the liquid and d that 
of the vapour. If we multiply both sides by M, the molecular 


weight, we get y* = constant; and this constant, which 

D d 

may be taken to be the molecular volume measured at a standard 
internal pressure, is called by Sugden the parachor* The values 
of this new constant show the same kind of additive and con- 
stitutive relations as those of the uncorrected molecular volume, 
the value for a molecule being expressible as the sum of a series 
of terms for the constituent atoms, together with others for par- 
ticular forms of linkage, such as a double bond or a closed ring ; 
but the agreement is much closer, and the difficulty of selecting 
comparable temperatures is removed, since the parachor is 
independent of the temperature. The following table shows the 
values for some of the commoner elements, and also for those 
constitutive influences which have to be taken into account ; 
these latter are in the first instance confined (apart from a small 
correction for the ester group) to the effects of unsaturation and 
ring-closure, which have recently 3 been shown to conform to a 
simple rule : if N is the number of hydrogen atoms required to/ 
convert the substance into a saturated open-chain compound, \ 

1 Sugden, J. C. S. 1924, 125, 1185 : Sugden, Reed and Wilkins, ibid., 
1925, 127, 1525 : Sugden and Whittaker, ibid., 1868 : Sugden and Wilkins, 
ibid., 2517. 

2 It might have been expected that in order to allow for the effect of 
internal pressure it would be necessary to know the compressibilities as 
well ; but the agreement between the calculated and observed values of 
the parachor shows that this provides a valuable means of determining the 
structure which is independent of a knowledge of the compressibilities. 

3 Sugden, J. C. S. 1927. 

126 Co-ordination Compounds 

and Z the number of atoms in the ring (taken as two for double 
and single links), then the increase of the parachor for the mole- 

cule- 28-2x5 

Elements Constitutive terms. 







Double link 






Triple link 




















O 2 in esters 60-0 (theory for two oxygen atoms and one double link 63-2). 

The theory was tested with some 200 liquids, mainly organic, 
and the calculated values agreed with the observed usually 
within 1 per cent., and practically always within 2 per cent. 1 
So close an agreement gives one great confidence in the sound- 
ness of the method. 

When however an extensive series of doubly-linked com- 
pounds was examined, it was found that they fell into two 
classes: whilst a large number (containing the groups C = C, 
C=fO, C=S, N=0) gave results in accordance with the theory, 
others did not ; instead of showing an increase for the double 
link of 28-2 units (within one or two units out of a total 
parachor of 100-300), they showed a small decrease, amounting 
on the average to -1-6. The difference between the two classes 
is far outside the limits of experimental error, and the distinc- 
tion is quite sharp ; the compound either shows the large rise or 
the small fall, and never an intermediate value. It is therefore 
clear that the ' double bonds ' of the traditional formulae repre- 
sent two different kinds of link. We have already come to the 
conclusion, on quite different grounds, that this is so : there is 
the true double link of four shared electrons, and the co-ordinate 
link (two shared electrons) of type (1) (with a divalent atom like 
oxygen as acceptor, as in the amine oxides), which, as we have 

1 As an example we may take propylene C 3 H e . The calculated value 
for the parachor is3x48+6x!7-l +23-2 (for the double bond) = 140-2 
The observed value is 189 9. 

Sugden's Parachor 127 

seen, was also written in the structural formulae as a double 
bond. The parachor provides us with a means of distinguishing 
between them. The molecules which give an increase of 23-2 
obviously contain true double links (the increase is exactly re- 
peated if the double link is replaced by a triple link), while those 
which give a fall of 1-6 contain a co-ordinate link : there is no 
double link to increase the parachor, and the small diminution 
is presumably due to electrostatic attraction. 

The structures which these measurements indicate are shown 
in the following list of formulae (R = alkyl or aryl). 

RCH=CH-R : R 2 C=O : (RO) 2 C=O : S=C=S 

R.N=C=S : R-O-N=0 

>0 9 / 

R-N< : R N<f : R N=N R : R-CH=N< 
^ ^ ^ 

* X - 

- - 

C1S->0: C1S 

Apart from the case of osmium tetroxide, which will be dis- 
cussed later, these conclusions are very satisfactory, because they 
entirely confirm the other evidence. All the double links in 
which one or both the atoms are carbon are shown to be real,! 
'with four shared electrons. The contrary suggestion of Lowry, 
that this link should be written as co-ordinate, is extremely 
improbable, since it implies at once the reduction of an octet to 
a sextet, and a disturbance of the electrostatic equilibrium, and 
also ascribes to the molecules electrical and stereochemical pro- 
perties which they do not possess. On the other hand, we have 
proof that the covalency of nitrogen cannot exceed four, so that 
the NO 2 group in the nitro-compounds and in the nitrates (but 
not in the nitrites) must have a co-ordinate link. With phos- 
phorus and sulphur, although the covalency can rise above four, 
there is strong evidence that it does not do so in most of the 
compounds with oxygen ; and the presence of a co-ordinate link 


in the sulphinates B )>S->O is directly confirmed by the 

stereochemical evidence (see Chapter XIII). 

128 Co-ordination Compounds 

The singular point about Sugden's results is that in every 
instance they involve the maintenance of the octet. They rule 
out on the one hand the co-ordinate link for carbon, where it 
implies the reduction of the octet to a sextet, and on the other 
the older formulae for the compounds of nitrogen, phosphorus, 
and sulphur, where these assume a covalency higher than 
four, and hence an expansion of the valency group beyond 

The one compound for which Sugden's conclusions appear to 
me to be incompatible with the other evidence is osmium 
tetroxide, because this is the only molecule he has dealt with in 
which there is reason to suppose a valency group larger than 
eight. The parachor for osmium tetroxide is 154-0. The value 
for oxygen is 20-0. If we assume that the osmium has an octet, 
there must be four co-ordinate links in the molecule 

0* *0 

^Os< , 
(T ^0 

and the value for Os will be : 

Os = 154-0 4 X 20-0 + 4 X 1-6 = 80-4. 

On the other hand, if the molecule is analogous to OsF 8 , and has 
four true double links 

CL .0 

we should have, according to Sugden's values : 

Os = 154-0 80-0 4x23-2 = 18-8 

We have no other evidence of the value of the parachor of 
osmium, but from very rough data for neighbouring elements 
we should expect to find it between 60 and 100. Hence Sugden 
concludes that the first formula is correct! The arguments in 
favour of the eight-covalent structure will be given later : the 
most obvious are the relation to the octofluoride and the vola- 
tility (boiling-point 100, molecular weight 255). Sugden's argu- 
ment seems at first sight conclusive, but on examination it will 
be seen that there is a difficulty. In the first place, the close 
agreement between theory and observation which he obtains 
with the other substances cannot be adduced here, for lack of 

Sugderis Parachor 129 

other data as to the parachor of osmium. Secondly, in all the 
substances for which the agreement was found to be close, the 
evidence shows the presence (in every atom except hydrogen) 
of an octet. We have therefore no proof that his values hold 
good when the valency group expands ; we should in fact expect 
that this would affect the molecular volume, and that in addition' 
to the constitutive factors of the parachor already mentioned, 
another would be needed to allow for the change in size of the 
valency group. This would presumably be negative : the high 
stability and screening effect of the octet as compared with any 
other arrangement of the outer electrons suggest that when there 
is a larger valency group the external field is stronger, and the 
attached atoms are more closely held ; just as we find that in 
zinc, where the group next to the valency electrons is eighteen, 
the volume is much smaller than in calcium, where it is eight. 
In osmium tetroxide, if the metal is really eight-covalent, we 
have an extreme case of this effect, since the valency group has 
expanded from eight to sixteen ; and we may conclude that if 
this occurred, it would considerably reduce the parachor, so that 
the fact that such a formula would give a negative value for the 
parachor of osmium if no allowance is made for the change in 
the valency group, is not conclusive evidence that the formula 
is wrong. 1 

If no more than this could be said, the objection might be 
thought fanciful. But there is definite evidence in its favour. 
Sulphur trioxide (in the monomenc form) may have any one of 
three formulae, which are given below, with the size of the 
valency group in the sulphur, and the parachor calculated on 
Sugden's values : 

-0 ,0 ,0 

I. O=S< II. O=Sf III. 0=SC 

\o *o x) 

Val. Gp. 8 Val. Gp. 10 Val. Gp. 12 

P = 129-0 P = 158-4 P = 177-8 

1 There is no intrinsic improbability in a negative parachor value for 
a particular atom : what is called the parachor of an atom is really the 
change in the parachor value for the whole molecule caused by the intro- 
duction of that atom, and if it causes the other groups to approach more 
closely, the total effect may be a contraction, just as an alkaline oxide has 
a smaller molecular volume (the parachor is of course unknown) than the 
metal it contains. 

3061 g 

130 Co-ordination Compounds 

The work of Le Blanc and of Smits 1 has shown that sulphur 
trioxide, even in the low melting a-form, is a mixture of more 
than one modification, and that the proportions vary with the 
temperature ; so we should not expect very constant or very 
concordant values of the parachor, but we should expect, if 
Sugden's view is right, that they would come between the limits 
given above, of 129-178. Berthoud 2 has measured the surface 
tension and the density of sulphur trioxide over a considerable 
range of temperature, and from his results the following values 
of the parachor can be calculated : 

at 19 P = 100-4 
at 44-9 P = 103-4 
at 78 P = 106 2 

Thus the observed value is lower than that calculated for any 
of the three possible formulae : indeed it is lower than the sum 
of Sugden's values for one sulphur and three oxygen atoms 
(without any allowance for the linkage), which is 108-2. This 
strongly suggests that an increase in the valency group causes 
a considerable diminution in the parachor, and that until we 
know how much allowance should be made for this, we cannot 
employ the method for the determination of structure except 
when the observed values agree closely with those calculated on 
the assumption that the octet is maintained : for it is very im- 
probable that the term representing the change in the valency 
group would happen exactly to counterbalance in every case that 
required by the change of linkage. 

Sugden's method thus promises to be of great value for the 
determination of structure ; but it cannot be fully applied until 
we know the effect of a change in the valency group. This can 
only be learnt from the examination of substances with atoms 
of a covalency greater than four. The experimental difficulties 
are unfortunately great : the preparation of compounds like 
sulphur hexafluoride or osmium octofluoride and the measure- 
ment of their surface tensions are not easy ; but we may hope 
that these difficulties will soon be overcome. 3 

1 Le Blanc and Ruhle, Ber. Sachs. Ahad. Wiss. 1922, 74, 106 : Smits and 
Schoenmaker, J. C. S. 1924, 125, 2554. 

2 Helv. Chem. Ada, 1922, 5, 513. 

3 Sugden's latest results (J.C.S. 1927, 1173) would seem to support these 
conclusions, although he interprets them differently. He finds the parachors 
of antimony and phosphorus pentachlondes to be 26 units lower than the 

Sugderfs Parachor 131 

sum of the atomic constants. On the theory we have adopted, the central 
atoms of these molecules have valency groups of 10, and so a diminution of 
the parachor is to be expected. Sugden maintains the ' octet rule ', that 
the valency group cannot exceed 8, and hence supposes that in these com- 
pounds two of the chlorine atoms are attached by 1 -electron links. He 
points out that the change from a link of four shared electrons (X = O) 
to a co-ordinate link of two (X->O) with the consequent electrostatic 
displacement, causes a fall in the parachor of 28 2 + 1-6 = 24 8. He argues 
that the change from a normal covalency to a 1 -electron link might be 
expected to cause half as great a fall, so that if the pentachlondes con- 
tained two 1-electron links in the molecule, the fall should be 24-8, which 
is very nearly what is observed. The numerical agreement is remarkable, 
but it is not a sufficient reason for adopting the ' octet rule ' in the face 
of the other evidence, if there is any relation between the structure of a 
link and its stability. As we have seen, the 1-electron link, in those few 
molecules in which it is undoubtedly present, is very unstable, while the 
octet rule would require us to assume the presence of four such links in 
sulphur hexafluonde, one of the most stable of known compounds. 


term association, especially in connexion with liquids, 
is familiar, and various properties which it involves are easy 
to enumerate, but they are more difficult to relate rationally to 
one another. They become easier to understand when we realize 
that such substances are essentially co-ordinated compounds, 
and that their behaviour depends on that fact. It will therefore 
be convenient to discuss these compounds here, and also to con- 
sider the relation of their properties to the general problem of 

It has long been known that liquids tend to fall into two 
classes, of which water and the hydrocarbons are extreme ex- 
riamples, the members of each class being as a rule more soluble 
;m one another than in a member of the other class. With the 
development of physical chemistry under the influence of van 't 
Hoff and Arrhenms, further differences between the two classes 
became evident. It was shown that liquids of the water class 
were ionizing solvents, that they had higher dielectric constants 
(which, as J. J. Thomson and Nernst pointed out, would account 
for their ionizing power), and that they tended to polymerize 
both in solution and in the pure liquid state, a tendency obviously 
related to their abnormally high boiling-points. The two classes 
therefore became known as associated and non-associated liquids. 
As more was learnt of the physics of the liquid state, and the 
theory of corresponding states, it was seen that while the be- 
haviour of non-associated liquids often approximated closely to 
that of an c ideal ' liquid, that of associated liquids departed 
widely from these simple laws, 1 which was indeed to be expected, 
since in their case the definition of the molecular weight was 
uncertain and variable. In the same way, while many of the 
properties of mixtures of non-associated liquids (for example, 
the specific volume, refractive power, and vapour pressure) are 
approximately, and sometimes almost exactly, the weighted 
means 2 of those of their components, this is not even roughly 

1 See Turner, Molecular Association, 1915, Chapter V. 

2 If a mixture contains the molecular fraction x of component A, for 
which the property has the value a, and hence 1 x of B, for which it has 
the value 6, the Weighted mean value for the mixture is x.a +(1 x).b. 

Molecular Association 133 

true of associated liquids. Hence the two classes are sometimes 
known as abnormal and normal. The terms ' polar " and ' non- 
polar ', which are now often applied to them, should be avoided, 
as they are ambiguous. They originated in a paper published 
by G. N. Lewis in 1913, 1 in which he distinguished two forms of 
chemical combination, differing ' not only in degree but also in 
kind ', a polar form, as exemplified in potassium chloride, and 
a non-polar, as in methane. In this paper, which contributed 
greatly to the recognition of the two forms of atomic linkage, he 
gives a list of the properties of each class of substances. While 
his non-polar class practically consists of what we should call 
non-associated covalent compounds, his polar class includes both 
salts and associated liquids. As a result of his work the terms 
polar and non-polar are commonly used of liquids to mean the 
same as associated and non-associated, or abnormal and normal : 
while these same terms are also used in a different connexion to 
denote electro valent and covalent molecules respectively. This 
leads to an unfortunate confusion of thought, since associated 
substances are not necessarily ionized or electrovalent, and in 
fact, according to later evidence, many of them are not ionized 
at all. It is true that associated liquids in the pure state usually 
have a minute conductivity (commonly less than 10~ 7 ), but as 
we now realize that weak electrolytes are weak because they are 
mainly in the covalent form (indeed Lewis suggests this in the 
paper in question) this is rather evidence against than for their 
being ' polar ' in the electrovalent sense. The ambiguity is best 
avoided by applying the terms polar and non-polar only to the 
forms of atomic linkage^ and calling these two classes of liquids 
either associated and non-associated, if we are mainly con- | [ 
cerned with their polymerization, or abnormal and normal, if ^ 
we are dealing with their general properties. 

Later investigations of the properties of associated as com- 
pared with non-associated liquids have furnished an immense 
number of new facts, but they cannot be said to have cleared up 
the question as a whole. The truth is that while no one doubts 
the existence of this distinction, and while the general order of 
substances is much the same whatever method of investigation 
is used, passing from an extreme example of association or 
abnormality like water through the lower and then the higher 
organic acids and alcohols to the ketones, ethers, and esters, and 
finally the aromatic and then the paraffin hydrocarbons, the 
1 J. Amer. Chem. Soc. 1918, 35, 1448. 

134 Molecular Association 

exact order obtained is somewhat different according to the par- 
ticular property on which it is based. The order of abnormality 
as determined by any of the usual methods of measuring associa- 
tion agrees with that of the dielectric constants and the ionizing 
powers on the whole, but not in detail. Even for the degree of 
association very diverse values are obtained according to the 
method used for determining it. 1 

The impossibility of finding any general measure of abnor- 
mality suggests that we are dealing with a selective action, that 
is, with chemical affinity : so that one associated solvent, for 
example, may be more abnormal than another in its action with 
one solute, and less abnormal with another. In all well-marked 
examples of associated liquids there is evidently a real combina- 
tion between the molecules, 2 and as these molecules are in the 
ordinary sense saturated, this must arise through the formation 
of co-ordinate links. The great majority of associated sub- 
stances contain a hydroxyl group ; and that the association 
depends on both the atoms of this group is evident if we com- 
pare, say, ethyl alcohol .with ethyl ether on the one hand and 
ethane on the other : in the absence of either the hydrogen or 
the oxygen of the hydroxyl group the association does not occur. 
The polymerization must therefore arise through this hydrogen 
acting as acceptor and the oxygen as donor, which would formally 
permit of .the linking up of an unlimited number of molecules : 

R R R R 

H O->H O->H O->H O->- ' 

It is not probable that the number so linked exceeds three or 
four. In water, for example, the structure of ice (presumably 
the highest polymer) points to three. 

There is evidence 3 that associated substances can be divided 
into two groups. In one, the association factor is limited to two, 
but this limit is nearly reached (in solution in non-associated 
solvents) at comparatively low concentrations. To this group 

1 See, for example, the list of values obtained by different methods in 
Walden's MolekulargrSsse von Elektrolyten, 1928, p. 58. 

2 This sometimes extends even to the vapour, as with formic and acetic 
acids ; water vapour probably contains from 6 to 10 per cent, of double 
molecules (Bose, Z. /. Elektrochem. 1908, 14, 269). But it is very difficult 
to detect a small amount of polymerization in the vapour, as an observed 
excess of the vapour density over that required by the simple gas laws 
may be due to the a of the van der Waals equation. 

8 See Auwers, Z. phys. Chem. 1899, 30, 300. 

Association due to Co-ordination 135 

the carboxylic acids belong : formic and acetic acids are largely 
dimeric even in the vapour at the boiling-point. 1 In the second 
group,' which includes alcohols and phenols, the degree of 
association is often less than with the first group in dilute solu- 
tion, but the polymerization can apparently proceed to a much 
higher limit : 2 the value of this limit cannot be determined, 
as the laws on which the molecular weight determinations are 
based no longer hold (see later, p. 149) m more concentrated 

Associated substances have all the characteristic properties of 
co-ordinated compounds, especially the low volatility and the 
high dielectric constant. The evidence of the volatility is some- 
times misunderstood, and it is said that the abnormally high 
boiling-points of these substances are explained by their poly- 
merization. But unless this is much greater than we have any 
reason to suppose, it will not account for the whole effect. For 
example, the ethers boil about 60 lower than the corresponding 
thio-ethers. Hydrogen sulphide boils at -61, and so uni- 
molecular H 2 O should boil about -120. If the real formula 
of water is H 6 O 3 (and it is very improbable that its average 
polymerization is even as great as this at 100), its true molecular 
weight is not 18 but 54. This will account for a rise in the boil- 
ing-point, but not for so large a rise as is actually found. Hydro- 
gen selenide (mol. wt. 81-2) boils at 42, and butane (mol. wt. 
58) at +1. Evidently the polymerized molecules themselves 
are much less volatile than corresponds to their molecular 
weights, as we should expect from the presence of the co- 
ordinate link. The high values of the dielectric constant (water, 
formamide, and hydrogen peroxide over 80, methyl alcohol 35, 
ethyl alcohol 27) are further evidence of co-ordination ; the 
ionization of an associated substance in the pure state is as 
a rule negligible, and there is no reason why the polymerization 

1 Drucker and Ullmann (Z.phys. Chem. 1910, 74, 004) have shown that the 
measurements of Ramsay and Young of the density of acetic acid vapour 
must be corrected for the amount absorbed on the glass surfaces. When 
allowance is made for this it is found that the vapour (at 80 110) con- 
tains roughly an equal number of single and double molecules. Formic 
acid appears to behave in the same way. It is doubtful whether ethyl 
alcohol vapour is associated under these conditions at all. 

2 For examples of this difference see the curves given by Brown and 
Bury, J. Phys. Chem. 1926, 30, 701. The arguments of these authors 
against the occurrence of polymerization in associated substances cannot 
however be regarded as valid. 

136 Molecular Association 

in itself, if it were not accompanied by the formation of co- 
ordinate links, should increase the dielectric constant. 

Other properties of associated liquids are direct results of the 
polymerization, such as their departure from the simple general 
laws deduced from the equation of state ; these laws are colh- 
gative they depend on the number of molecules present and 
the size of the molecule of an associated liquid is an uncertain 
quantity, and is a function of the conditions. The same may be 
said of their failure to comply with the mixture law. If two 
liquids A and B, each containing polymerized molecules, are 
mixed, these polymers will to some extent dissociate, and new 
complexes, containing both A and B molecules, will be formed, 
whose production will naturally modify the properties of the 
mixture. This also accounts for the considerable heat (and 
volume) effects often observed on mixing such liquids. With 
non-associated liquids, since there is no combination between 
the molecules, the components have little influence on one 
another, and their heats of mixing are usually negligible. 

Another characteristic tendency is that of solutes in non- 
associated liquids to associate, and in associated liquids to dis- 
spciate, whether by this we mean the separation of polymerized 
molecules into their unirnolecular constituents, or that of electro- 
lytes into their ions. There are two reasons for this : first that 
the high dielectric constant of the associated solvent weakens 
the attraction between the ions ; and secondly that an associated 
solute will tend to combine with an associated solvent. In 
dilute solution, with which we are mainly concerned, the com- 
plexes so produced will mostly not contain more than one simple 
molecule of solute apiece : if A is the solute and B the solvent, 
they will be AB n . The methods of determining molecular weight 
in solution really give not the molecular weight of the solute, 
but the number of molecules produced in solution by a given 
weight of solute ; they take no account of the weight of solvent 
combined with these molecules, which only affects the result 
when the solution is so strong that the amount of solvent thus 
withdrawn is appreciable. Hence where the actual molecules in 
solution are AB n , the observed molecular weight is that of A 
alone, and the solute is said to be dissociated into simple mole- 
cules. If this solute is dissolved in a hydrocarbon, which has 
no tendency to combine with it, the solute molecules are free 
to combine with one another. Combination with the solvent 
no doubt has a considerable effect in promoting the ionization 

' Donor ' Molecules 137 

of we.ak electrolytes : if the ions (or one of them) can combine 
with the solvent, the whole equilibrium 

M-A ; [M]A ^ 


[M, solvent] + 

will shift in the direction of ionization. The cation in particular 
is, as we have seen, often a powerful acceptor, and so is peculiarly 
ready to co-ordinate with a donor, which an associated liquid 
must always contain. 

The consideration of the abnormality of liquids from the point 
of view of co-ordination brings out a further point, which ex- 
plains some of the difficulties of the subject. The association, 
as we have seen, requires that each molecule should contain one 
atom which can act as a donor, and another which can act as 
acceptor : it is only when both are present that the substance 
can polymerize. But there are liquids whose molecules contain 
only a donor, and others in which there is only an acceptor. Such 
substances will not polymerize, and in the pure state will behave 
as normal liquids ; but in the presence of a second substance 
capable of association (and so possessing both kinds of atoms 
required for co-ordination) they may exert their powers as donors 
or acceptors, and will then behave abnormally. They thus have 
properties in common with each of the two mam classes of liquids, 
and their behaviour has been found difficult to explain. Acceptor 
liquids (if the phrase is permissible) are so unstable, being prone 
to accept water, and even atmospheric oxygen, usually with 
decomposition, that comparatively little is known of their 
physical behaviour in two-component systems : examples are 
boron tnfluonde, stannic chloride, and the zinc alkyls. But 
donor liquids are quite common, familiar examples being sulphur 
dioxide, nitrobenzene, and ether, They are not associated, 
because they have no acceptor, but they readily associate with 
a solute which has, as all associated solutes have, an acceptor 
alom. Ether, for example, is a normal liquid as judged by its ; ' 
properties in the pure state, but it is an abnormally good solvent i 
for many hydroxylic compounds, with which it combines like ' j 
an alcohol, its oxygen co-ordinating with the hydroxylic hydro- - 
gen : (C 2 H 6 ) 2 O->H O -R. Nitrobenzene again, although it 
is not associated (its high dielectric constant and its low vola- 
tility are due to the presence of a co-ordinate link in the simple 
molecule), behaves as an abnormal solvent with certain associated 

138 Molecular Association 

solutes, as will be shown in the next section. The peculiar pro- 
perties of amines, which are also difficult to place in the series 
of liquids, are probably to be explained by the molecule possess- 
ing strong donor and weak acceptor properties, so that its 
abnormality is slight in the pure substance, but can become 
strong in presence of a suitable solute. 


The most practically important difference between these two 
classes of liquids is in their solvent power. Speaking generally, 
a liquid is a better solvent for members of its own class than for 
members of the other, and associated liquids (including donors 
like sulphur dioxide) are practically alone in being able to dis- 
solve inorganic salts. While all non-associated liquids are in- 
finitely miscible with one another, and all extreme members of 
the associated class, such as water and the lower alcohols and 
acids, are also miscible with one another, water will only dis- 
solve to a very limited extent in non-associated liquids: and 
other pairs of a normal and an abnormal liquid, such as benzene 
and a lower alcohol, although they do not actually form two 
liquid layers, can be shown not to be far removed from separa- 
tion. We have seen that associated molecules, owing to the 
electrostatic disturbance resulting from the co-ordinate link, 
must attract one another. An attempt has been made to deter- 
mine the internal pressure to which this attraction gives rise, 
and to use it as a measure of the abnormality. Although this 
has not been much more successful than other attempts to 
obtain a quantitative value of abnormality, there is no doubt 
that the attraction exists. If such a liquid is mixed with a 
normal liquid like hexane, in which the molecules have a very 
weak external field, and consequently very little attraction for 
one another, there will be a tendency for the two kinds of mole- 
cules to separate, the associated congregating together, and as 
it were squeezing out the others. If this goes far enough, the 
liquid will separate into two layers. 

We can thus see why these liquids are imperfectly miscible. 
Usually however when we talk of solubility we are not thinking 
of the miscibility of liquids, but of the solubility of a solid in 
a liquid. In order to make it clear how this is affected by the 
character of the solvent and the solute, the general conditions 
determining solubility must be briefly reviewed. No more will 

Solubility 139 

be said of them than is necessary for the understanding of the 
question under discussion. 

A saturated solution being one which will dissolve no more 
solid, it follows that the vapour pressure of the solid at the tem- 
perature in question must be equal to the partial pressure of 
the same substance in the vapour from the solution, for if it 
were not, the solute would distil either from the solution to the 
solid or vice versa, and the two phases would not be in equili- 
brium. The solvent power will therefore be determined (at least 
in part) by the partial pressure of the solution. Suppose 1 we 
have a solvent A and a solute B at temperature T. T is obviously 
below the melting-point of the solute, but we may imagine that 
the solute can be obtained in a supercooled condition at this 
temperature, and that in this liquid condition it has a vapour 
pressure p. If increasing quantities of the solvent A are added 
to the superfused solute, its partial pressure will fall, reaching 
zero at the point A, where the solution is infinitely dilute. We 
shall therefore have (Fig. 3) a curve representing at temperature 
T the change of the partial pressure of the solute with con- 
centration. This will have one of the three forms given in 
Fig. 8 : it will either be a straight line (I), or it will lie above 
this (II : ' positive curve ') or below it (III : ' negative curve '). 
Now since the temperature is below the melting-point of the 
solute, the vapour pressure of solid B must be less than p, that 
of the supercooled liquid : let it be represented by TT. A hori- 
zontal straight line drawn through TT will cut the three curves 
at three different points, corresponding to the molecular con- 
centrations Sj, Sjj, S U j. These are the concentrations at which 
the partial pressure of B in the vapour from the solution is equal 
to the vapour pressure of solid B. Hence these must represent 
saturated solutions ; and S l9 S n , or S m will be the solubility (in 
molecular proportions) of B in A at this temperature, according 
as the partial pressure curve is I, II, or III. In other words, the 
amount of solvent in a saturated solution is that required to 
reduce the vapour pressure of the supercooled liquid solute as 
much as it is reduced by conversion into the solid form. This 
diagram is of fundamental importance to the understanding of 
the factors which determine solubility. They are obviously two : 
(i) the ratio TT /p of the vapour pressure of the solid solute at T 
to that of the supercooled liquid, and (ii) the shape of the partial 
pressure curve ; the first depending on the solute alone, and 
1 See Hildebrand, Solubility, 1924, p. 35. 


Molecular Association 

the second both on the solute and on the solvent. The first 
factor TT/P is determined by the molecular heat of fusion Q, 1 
the temperature of observation T, and the melting-point T , 
according to the equation 



T T 

Now Q usually lies between 4 and 7 kilogram-calories per gram- 

A Sjj Sj Sill 

Solvent Molecular concentration 

FIG. 3 


molecule, and very seldom is outside the limits 2-10 kgr. cals. 
T T may vary from 10 or less to 1000 or more. Hence the 
height of the melting-point has commonly much more effect on 

1 Strictly speaking, this is not constant, but falls slightly with the 
temperature, the coefficient being equal to the difference between the 
specific heats of the supercooled liquid and the solid, of which the former 
is always the greater ; and allowance should be made for this in the equa- 
tion which follows ; but the error introduced by neglecting it is usually 

Solubility 141 

this factor than the heat of fusion ; this is the basis of Car- 
nelley's rule, that of similar substances (that is, where the partial 
pressure curves are not very different) the one which has the 
lower melting-point is the more soluble. Two extreme examples 
may be taken : 

(i) For naphthalene at 25 (Q = 4-4 kgr. cals., T Q = 80) : 

TT/p - 0-31. 

(ii) For sodium chloride at 25 (Q - 7-22 kgr. cals., T = 
804) : TT/P - 0-000148 (about 1/7000). 

These values are the actual solubilities (in molecular fractions) 
which the substances would have at 25 in any solvent with 
which they gave the straight line partial pressure curve (I). 
With non-associated substances like naphthalene in solvents of 
the same type, the partial pressure curve very nearly is a straight 
line, and so the observed solubilities are often very near the 
calculated : thus that of naphthalene in benzene at 25 is (in 
molecular fraction) 29. 

The value of the solubility calculated in this way (from the 
heat of fusion) for any solvent with which the solute behaves 
ideally (giving a straight line partial pressure curve) is an 
important characteristic of the solute, and may be called its 
' natural solubility '- 1 The departure of the actual solubility in 
any solvent from this value is a measure of the departure of the 
partial pressure curve from a straight line. If the observed 
solubility is less than the ' natural ', the curve is of type II 
(positive) : if greater, it is of type III (negative). As examples 
we may take the solubilities of naphthalene and of sodium 
chloride in water and benzene, using the values of Trjp already 
obtained for these solutes. The solubility of naphthalene in 
water is minute, perhaps at the outside 1 gram per litre. That 
of sodium chloride in benzene is smaller still : it is too small to 
be measured, but we may take it to be of the order of 1 mgr. 
per litre. The observed and calculated values in grams per kgr. 

1 The following are the values in molecular percentages ( = TTJP x 100) 
of the ' natural solubilities ' at 25 of substances with heats of fusion of 
4 and 7 kgr. cals. per gr.-mol. respectively (the normal limits of variation), 
according to their melting-points : 

M. Pt. Q=4 k. cals. Q=7 k. cals. 

50 59 3 40-1 

100 25-9 9 42 

200 8 33 1-29 

500 1 58 071 

1000 0-57 012 

142 Molecular Association 

of solvent at 25 are as follows (the calculated values in water 
will depend on what we take as its molecular weight, since this 
affects the conversion of molecular into weight proportion) : 

Naphthalene : 

in benzene : calculated 788 : observed 708 : ratio 96 

in water : calculated (as H 2 O) 3200 , , ratio 0-00008 

(as H 6 3 ) 1100 : ODservea u L : ratio 0-0001 
Sodium chloride : 

in benzene : calculated 0-11 : observed 0-001 . ratio 0-01 
in water : calculated (as H,,O) 0-48 , , 0/} , ratio 750 

(as H 6 3 ) 0-16 : bserved 3G1 : ratio 2300 

The non-associated solute has in benzene nearly its * natural ' 
solubility, but in water only a minute fraction ; the ionized 
solute, whose natural solubility is much smaller, is still less 
soluble in benzene, but in water it is enormously more soluble 
than the calculation requires. This shows that the partial 
pressure curve of naphthalene is nearly a straight line in benzene, 
and is highly positive in water, while that of sodium chloride is 
positive in benzene, and highly negative in water. 

The next question is what are the causes of the various forms 
of partial pressure curves. Positive curves (which give unduly 
low solubilities) can be shown to be given by two components 
which are approaching the temperature at which they will 
separate into two layers ; they are therefore due, as has already 
been explained, to a large difference in the internal pressures 
of solvent and solute. Straight line curves of course indicate 
that the molecules are indifferent to one another, which can only 
happen if both components are of the normal, non-associated 
type. Negative curves (abnormally high solubility) can only be 
explained by supposing that some kind of combination occurs 
between the components. In an extreme case, as with the 
partial pressure of methylamine in presence of a sulphonic acid, 
the combination will be complete until an equimolecular mixture 
is reached : the salt will not be dissociated into its components 
at all, and up to this point there will be no partial pressure of 
the amine whatever ; the curve will fall from p, the value for 
the pure amine, to zero at 50 molecules per cent, (ps, Fig. 4). 
With a weak acid and base (say ammonia and hydrocyanic acid) 
the salt will be largely dissociated into hydrocyanic acid and 
ammonia ; there will be a perceptible vapour pressure at 50 
per cent., and the curve will be smoothed off, as at x in the 



figure. Thus when the solute combines with the solvent, the 
curve must lie between ps and the straight line pA., being always 
negative (the solubility greater than the natural), and approach- 
ing the straight line as the combination becomes weaker. 

On these principles we can see what will be the general effect 
on the solubility of the character of the solvent and the solute 
respectively. We have to consider two kinds of solvent, non- 
associated and associated, and three kinds of solutes, non- 






Molecular concentration 
FIG. 4 

associated, associated, and ionized ; true liquid salts can only 
exist at high temperatures (with the possible exception of a few 
strong acids such as perchloric), and they need not be considered 
as solvents. 

The ' natural ' solubility depends mainly on the melting-point 
of the solute : if this is high, it will be small, and if low, large ; 
if the solute is liquid (i. e. at or above its melting-point) the 
natural solubility is of course infinite. A high melting-point is 
caused (i) by an attractive force between the molecules and 
(ii) by a high molecular weight. Hence non-associated sub- 
stances (with normally covalent molecules) will have low melting- 
points unless their molecular weights are large. Associated 

144 Molecular Association 

substances (co-ordinated) will have their melting-points raised by 
the increase of molecular weight caused by the association, and 
probably also by the attraction due to the co-ordinate links : 
but experience shows that neither of these produces a large 
effect. Ionized substances (those which are still ionized in the 
solid state) will have high melting -points owing to the large force 
between the charged ions. 

The relation between the natural solubility and that observed 
in a particular solvent depends on the shape of the vapour pres- 
sure curve. With non-associated solutes in non-associated sol- 
vents this approximates to a straight line, and the solubilities 
come near to the natural. With the same solutes in associated 
solvents, especially in water, the vapour pressure curve is 
strongly positive, owing to the tendency to separation, and the 
solubilities are therefore below, and often far below, the natural. 
Associated (co-ordinated, not materially ionized) solutes in non- 
associated solvents tend for the same reason to have positive 
partial pressure curves and an abnormally low solubility : but 
against this must be set the rise in molecular weight, which in- 
creases the weight per cent, dissolved, and also the apparent 
molecular percentage, if the simple formula weight is taken (as 
it practically must be) to represent the molecule. In associated 
solvents their solubilities are increased, owing to their cross- 
association with the solute. Ionized solutes, on account of their 
high internal pressure, give highly positive partial pressure 
curves in non-associated liquids, and so have a solubility much 
below the natural : and as this last is already small on account 
of their high melting-points, they are as a rule almost if not 
quite insoluble in such solvents. 1 In associated liquids they tend 
to give negative curves, owing both to the effect of the high 
dielectric constant on the force between the ions and to the 
tendency of the ions to solvate. Hence their solubilities in these 
liquids may reach very high values. 

' Pure donors ' like sulphur dioxide and ether behave as normal 
substances in presence of normal, and as associated in presence 
of associated substances. 

These conclusions are of value not only from the point of 

1 The peculiar solubilities shown in non-associated liquids like chloro- 
form by certain undoubted salts, usually of complex (as ammonium or 
sulphomum) cations seem to be due to the formation of something like 
a colloidal solution. The solute molecules are apparently charged, but are 
highly polymerized. See Walden, loc. cit. 

Solubility and Structure 145 

view of the general theory, but also because they enable us to infer 
from the solubility whether a molecule contains co-ordinate or 
ionized links or neither. If it contains neither, it will show its 
usually considerable natural solubility in solvents like benzene, 
and will be much less soluble in water. If it contains co-ordinate 
links not due to association (like the chelate compounds described 
on p. 119), and has no donor or acceptor atom, its solubility will 
as a rule be that of a non-associated substance. The behaviour 
of associated substances, which usually means those containing 
hydroxyl groups, is sometimes perplexing. The melting-points 
may, for reasons not fully understood, be low, and even very low, 
and hence the natural solubility large : this however is known and 
can be taken into account. The association tends to make these 
substances less soluble in hydrocarbons and similar solvents, 
especially if the associating groups (as hydroxyl) form a large pro- 
portion of the molecule, and the internal pressure is high ; but if 
they have a large ' organic ' constituent (covalent non-co-ordinated 
radical), as in the aromatic acids and the higher alcohols, this 
diminishes the internal pressure, and they may become compara- 
tively insoluble in water ; in that case they often dissolve more 
readily in ether or alcohol than either in water or benzene. Finally, 
salts are practically insoluble in non-associated liquids, and as a 
rule far more soluble in water than in any organic solvent, even 
a lower alcohol, and far more than we should expect from their 

Some examples may be given of the practical application of 
these ideas. 

(i) Distinction of ionized and covalent links. The sodium 
derivative of benzoylacetone 1 might either be a salt (I) or a 
covalent chelate compound (II) : 

C 8 H 5 -C-0 [Na] 
" 5 

C,H 8 -C 

I. || II. CH 

CH-CO CH 3 \ / 

CH 3 -C=0 

It is found to char on heating without melting, to dissolve readily 
in water, and to be quite insoluble in benzene and toluene. All 
these properties are those of a salt, and so we may assume that 
it has the formula I. If it is recrystalhzed from aqueous alcohol, 
it takes up two molecules of water. This might be ' water of 

1 Sidgwick and Brewer, J. C. S. 1925, 127, 2379. 

3063 U 

146 Molecular Association 

crystallization ' in the sense that it was attached to the sodium 
ion in formula I, giving [Na, 2H 2 0] + . If so, the solubility of 
the hydrated compound should be of the same order as that of 
the anhydrous salt. But the hydrate is found to dissolve in 
toluene. This is a clear proof that it is not an ionized but a 
covalent compound, and its structure must be 

A rather less obvious example is that of the acetylacetonate oJ 
dimethyl thallium. 1 The iodide of this base (CH 3 ) 2 T1I, is ar 
undoubted salt, derived from the strong base [(CH 8 ) 2 T1]OH 
Here again, therefore, the diketone compound might either be 
a salt (I) or a chelate compound (II) : 

CKr-C CH, 


CH 8 -C=0 CH 3 

The compound has a fairly low melting-point, can be sublimec 
easily in vacuo, and is readily soluble in benzene. All these pro 
perties make it clear that the molecule is covalent, and the secon< 
formula correct. We should therefore expect that the substand 
(like beryllium acetonylacetonate) would be slightly if at al 
soluble in water. It is found however to dissolve readily 
Formula II has no associating groups such as hydroxyl t 
account for this solubility, and the only possible explanation i 
that the molecule, which alone and in benzene has the structur 
II, changes in water into the ionized form I. This hypothesi 
is easily tested. If in water the compound is ionized, then sine 
it is the salt of a strong base and a weak acid, it should b 
hydrolyzed, and have an alkaline reaction : this it is found t 
have. Also the solution must contain. [(CH 3 ) 2 T1] + ions, an. 
therefore give with potassium iodide a precipitate of the slightl 
soluble iodide of this base ; this also it does. 

(ii) Distinction between associated and non-associated suh 
stances. An example of this is afforded by the case of thos 
compounds (such as the /?-diketones, and certain ortho-sul 

1 Unpublished work. 

Solubility and Structure 147 

stituted phenols, like salicylic aldehyde) which can form chelate 
^ derivatives with metals, of such types as 

R-C O X\/\ 

X and | T 

CH X and 



There is no doubt that they form ring structures of this type if 
X is an appropriate metal : the question is whether they do so 
also when X is hydrogen. This is of importance from its bearing 
on the maximum co valency of hydrogen. It can be answered 
by investigating the association of the compounds. If the 
hydrogen compound is not co-ordinated, it will contain a free 
hydroxyl group, and hence be an associated substance ; if it is 
co-ordinated, as in the above formulae (X - H), the acceptor 
properties of the hydroxylic hydrogen are used up, and the sub- 
stance will be non-associated. Thus the effect of the chelation 
should be to increase the volatility, and to make the solubility 
greater in non-associated solvents and less in associated. To 
find whether this effect is produced, the substance must be com- 
pared with analogous compounds. The nearest analogues of the 
enolized jS-diketone derivatives are the isomeric ketonic forms 
R-C=CH-C-R . R-C-CH 2 -C-R 


Enolic Ketonic 

These true diketones are in the strict sense non-associated, and 
behave as fairly normal substances, certainly more so than 
definitely hydroxylic compounds. Experiment shows that the 
enolic form is actually more volatile (where this property can be 
measured) than the isomeric ketone, and that in all cases the 
ratio of the solubility of the enol to that of the ketone is greatest 
in the least associated liquids like the hydrocarbons, and less in 
water and the alcohols. Thus the enols behave even less like 
associated liquids than the ketones, and cannot have a free 
hydroxyl group : they must be, at any rate to a very large 
extent, chelate compounds, with the hydrogen co-ordinated to 
the second oxygen atom. 1 

In the ortho-substituted phenols 2 we can institute a closer 

1 Sidgwick, J. C. S. 1925, 127, 907. 

2 Sidgwick and Ewbank, J. C. S. 1921, 119, 979 . Sidgwick and Callow, 
ibid., 1924, 125, 527. 

148 Molecular Association 

comparison, with the isomeric meta- and para-compounds ; 
these cannot be chelated, because an aromatic derivative cannot 
form a meta- or para-ring, and so they show how such a molecule 
behaves when its hydroxyl group is available for association. 
The results show that whenever the substituent has the necessary 
structure to form in the ortho-position a chelate six-ring through 
the hydroxyl hydrogen as with 

r /H r /OR K ^O 

-C<^ , -C^ o , or -N<^ o , 

the ortho isomers differ markedly from the meta and para, and 
always in the direction of being less associated ; they are more 
volatile, and are more soluble in benzene 1 and less in water. 
The evidence for co-ordination of the hydrogen is conclusive. 
There is another remarkable point about these phenols, bearing 
on the general question of association. Auwers 2 has examined 
the effect of such groups as NO 2 and CHO on the cryoscopic 
properties of the phenols. The determination of the molecular 
weight of a phenol by the depression of the freezing-point of 
a non-associated solvent like benzene gives the usual indication 
of the association of a solute, that the molecular weight rises 
rapidly with increasing concentration. Auwers finds that an 
active group like NO 2 or CHO can produce three different 
effects. If introduced into the solute (phenol) in the ortho- 
position it makes it less associated : the rise of molecular weight 
with concentration becomes less or nothing. In the meta- or 
para-position in the solute it increases the association. Finally, 
if it is introduced into the solvent (for example benzene) it 
makes an associated solute appear less associated : the molecular 
weight as measured cryoscopically rises less with concentration in 
nitrobenzene than in benzene. The order of efficiency of different 
substituting groups is the same for all these three phenomena. 
These facts are all in accordance with the views which we have 

1 In water the system generally forms two layers, and the critical solu- 
tion temperature is then a direct measure of the solubility. In benzene 
this seldom happens, and the solid-liquid curves obtained are of course 
determined by the ir/p values, which largely depend on the melting-points, 
and are not the same for different isomers. This difficulty can be overcome 
by calculating from the solubility curves the apparent heat of solution at 
various concentrations. If the partial pressure curve approaches a straight 
line, this value will be nearly constant : if it is a positive curve (indicating 
in benzene that the phenol behaves as an associated substance) the heat 
values will rise to a maximum (see Sidgwick and Ewbank, loc. cit ). 

2 Z. phys. Cham. 1903, 42, 513. 

Solubility and Structure 149 

adopted. Phenol itself is associated in benzene, through the 
oxygen of the hydroxyl as donor and the hydrogen as acceptor : 

9e H 5 9 flHfi 9 6 ^ 5 A. 

I I I . &c. 

H O-^H O-J-H 0-> 

An * active ' group is one which contains an active donor, like the 
oxygen in NO 2 and CHO. In the ortho-position in the phenol 
this, as we have seen, forms a chelate ring with the hydroxyl 
hydrogen of the same molecule, and hence prevents association 
with other molecules, since the hydrogen has acquired its maxi- 
mum covalency. In the meta- or para-position in the phenol the 
active group is still able to form a co-ordinate link, but it cannot 
do so with the hydroxyl hydrogen of the same molecule, since 
this would involve the formation of a second ring attached to 
the benzene nucleus in the meta- or para-position, which (no 
doubt for steric reasons) is impossible. But it is able to co- 
ordinate with the hydrogen of the hydroxyl group in another 
molecule, and does so more readily than a hydroxylic oxygen 
atom : hence the meta- and para-compounds are more associated 
than phenol itself. If we introduce the active donor group into 
the solvent (benzene) instead of the solute, we make the solvent 
able to co-ordinate with the solute, if that is a phenol or other 
hydroxylic compound, 

It will therefore tend (being in large excess) to break up the 
phenol aggregates : the number of solute molecules will increase, 
and the ' molecular weight ', as determined cryoscopically, will 

There are one or two further points about associated liquids 
which should be mentioned. The cryoscopic evidence of associa- 
tion the fact that the freezing-point of a solvent is less depressed 
by a solute than its formula weight requires must be inter- 
preted with caution. This effect is always found when the partial 
pressure curve is positive, and with a system of associated + 
non-associated substance (for example, benzene + para-nitro- 
phenol) it is found at both ends of the freezing-point curve for 
a dilute solution of benzene in the nitrophenol as well as for the 
reverse case since the partial pressure curves of both com- 
ponents are positive. It cannot be supposed that the benzene 
is actually associated in this solvent, and the freezing-point 
results obviously mean only that the system is approaching the 

150 Molecular Association 

condition of separation into two layers. It is true that this 
implies that one component is associated, and in that sense we 
may say that the cryoscopic method truly indicates association, 
but it is not necessarily association of the component whose 
molecular weight is being determined. For the same reason 
where polymerization undoubtedly occurs, the absolute values 
of the association factor which the cryoscopic method gives 
cannot be accepted as true except where they are reasonably 
constant over a range of concentrations. The apparent molecular 
weight of methyl alcohol in benzene solution as calculated from 
the depression of the freezing-point rises to some thirty times 
that of the simple formula : this does not mean that thirty 
CH 3 OH molecules actually combine to one, but only that the 
partial pressure curve is highly positive. "With associated solutes 
of the carboxylic acid class, where the apparent molecular weight 
rises rather rapidly to twice the simple value, and does not 
further increase, the results can no doubt be accepted as true. 

Another point which should be noticed is the remarkable 
difference in solvent properties between the aromatic hydro- 
carbons and the paraffins. One is inclined to regard both groups 
as representing the extreme of non-association or normality, but 
in fact there is almost as much difference between them as 
between benzene and alcohol. The paraffins have an extra- 
ordinarily small solvent power, especially for those somewhat 
associated substances which, owing to a large ' organic ' con- 
stituent, are readily soluble in benzene : they are only slightly 
miscible (even above the melting-point of the solute) with many 
(not ortho) aromatic hydroxy-acids, with all three nitrobenzoic 
acids, and even with aniline. Again, while they are miscible 
with the lower alcohols, a very small trace of water causes 
separation into two layers, whereas with benzene and alcohol 
much more can be added : for example, ethyl alcohol contain- 
ing 10 per cent, of water will dissolve four times its weight of 
benzene, but only a third of its weight of hexane. Naphthenes 
(cyclohexane derivatives) are intermediate in this respect 
between the aromatic hydrocarbons and the paraffins. The 
reasons for these differences are not known : they are presum- 
ably due to the external field of the molecules (and hence the 
internal pressure) being much weaker with the paraffins ; but 
the difference in dielectric constant is not large (about 1-8 for 
the paraffins and 2-8 for the aromatic hydrocarbons), and 
scarcely seems enough to account for the contrast. It is possible 

Solubility and Structure 


that the formation of a positive vapour pressure curve depends 
not on the difference of the internal pressures or dielectric con- 
stants of the components, but on their ratio. 

There is one class of liquids which has not been mentioned, 
namely liquid metals. They consist of positive (not necessarily 
monatomic) ions and electrons. No question arises as to their 
solubility (in the ordinary sense of the term) in non-metallic 
solvents : they can only dissolve as ions, and the electrostatic 
forces so produced prevent the process from proceeding beyond 
the surface layer unless they are relieved by chemical changes 
taking place. Solution of a metal in the sense in which we have 
been using the term can only take place in another metal. Such 
solutions are outside the sphere of our discussion. It may how- 
ever be pointed out that separation into two liquid layers is not 
uncommon among metals (especially alkali metals), probably on 
account of the high internal pressures which prevail in them. 


/CHEMICAL combination consists, as we have seen, in the 
^^redistribution of the electrons among the atoms forming 
a molecule so as to produce more stable groupings, this being 
effected in three ways by the formation either of electrovalencies 
or of normal or co-ordinate covalencies. We have considered the 
mechanism of each of these forms of linkage, with the properties 
to which it gives rise, and the means by which its presence can be 
detected. We have now to consider the electronic groupings so pro- 
duced : to inquire what groupings are experimentally found to be 
stable, and how these can be related to the structure of the atom. 

We may take first the limits to the size of the valency group. 
We know that an atom can increase its covalency even after all 
its own valency electrons are used up, by forming co-ordinate 
links as an acceptor, and that a valency group of sixteen a 
covalency of eight is possible for some atoms, as for osmium 
in the octofluoride OsF 8 . If so large a group can be formed by 
atoms in general, it would seem that the possibilities of chemical 
combination are extraordinarily wide. There is however evi- 
dence that this is not so, and that the size of the valency group, 
or the number of covalencies which an atom can form, is subject to 
limits which vary with its position in the periodic table. These 
limits, which could not have been deduced from our present know- 
ledge of atomic structure, but are founded solely on the chemical 
evidence, may be stated first, and the evidence then discussed. 

It appears 1 that the maximum covalency of an atom is : 

(i) For hydrogen 2 (4 shared electrons). 

(ii) For the elements of the first short period of the table 
(from lithium 8 to fluorine 7), 4 (8 shared electrons). 

(lii) For those of the second short period (sodium 11 to chlo- 
rine 17) and the first long period (potassium 19 to 
bromine 35) 6 (12 shared electrons). 

(iv) For the heavier elements (rubidium 37 to uranium 92) 
8 (16 shared electrons). 

There are faint indications of the possibility of a covalency of 
10 in certain elements after the end of the second long period, 

1 Sidgwick, Trans Faraday Soc. 1923, 19, 469 : Sidgwick and Callow, 
J. C. S. 1924, 125, 582. 

Covalency Maxima 153 

but they are not conclusive. It will be seen that this division 
cuts across that of the ordinary group valencies, and depends 
not on the group to which an element belongs, but on its period. 
The evidence for this rule is as follows : 

(i) With hydrogen we have already seen that there are many 
reasons for believing that by co-ordination it can acquire a 
covalency of two : to take only the more conspicuous instances, 
this must be assumed to explain the structure of hydrofluoric 
acid and of ice, the association of hydroxylic compounds in 
general, and the chelate structure of the enolic forms of 0-di- 
ketones and various ortho-substituted phenols . A higher covalency 
than two for hydrogen has never been seriously suggested. 

(ii) Of the elements in the first short period (Li -F) all except 
fluorine x have been obtained in a four-covalent form : for 
example, lithium benzoyl acetone with two molecules of water, 
analogous to the sodium compound whose formula is given on 
p. 146 : beryllium acetylacetonate BeA 2 : boron in C1 3 B-NH 3 : 
innumerable compounds of carbon and of nitrogen : and oxygen 
in the ' basic * beryllium acetate Be 4 0(0 CO CH 3 ) 6 , a purely 
covalent compound, in which the unique oxygen atom can be 
shown to be attached to all four beryllium atoms. That the 
covalency of these elements cannot exceed four was maintained 
by Werner, 2 and is supported by a great mass of evidence. We 
may take first that relating to carbon and nitrogen, the elements 
of which we know most. Among the enormous number of known 
compounds of carbon there are none which involve a higher 
covalency for the carbon than four. Attempts have been made 
to induce carbon tetrafluoride to form addition compounds of 
the type so readily given by silicon tetrafluoride (for example, in 
the fluosilicates) but they have all failed. For nitrogen also the 
negative evidence is very extensive ; it is supported by Sugden's 
proof of the co-ordinated structure of the nitro-compounds and 
alkyl nitrates, and particularly strongly by the behaviour of the 

i That fluorine should be especially reluctant to assume a high covalency 
follows from the theory of Fajans. It forms a negative ion of small charge 
and small size. Both of these properties make the conversion of the electro- 
valency into a covalency difficult, and we have already seen that fluorine 
ionizes in positions in which chlorine and the other halogens do not, as in 
aluminium and stannic fluorides. A covalency of more than 1 is almost 
unknown for fluorine, and is perhaps limited to the higher polymers of 
hydrofluonc acid, such as H 3 F 3 , which presumably must be written 

2 Werner of course called it the co-ordination number. 

3061 X 

154 Covalency Maxima 

recently discovered group of compounds in which nitrogen has 
been made to combine with five hydrocarbon radicals, as in the 
triphenylmethyl and benzyl compounds of tetramethyl-am- 
monium (C 6 H 5 ) 3 C[N(CH 3 ) 4 ] and C 6 H 5 CH 2 [N(CH 3 ) 4 ]. 1 These 
compounds have all the characteristics of salts : they are bright 
red, which for a purely covalent compound of this composition is 
inexplicable, they are instantly decomposed by water to give the 
aromatic hydrocarbon and tetramethyl-ammonium hydroxide, 
and they form conducting solutions in pyridine. The incapacity 
of the nitrogen atom to form more than four-covalent links is so 
complete that it overcomes the reluctance of the carbon to ionize, 
and the products exhibit the colour and the extreme unsaturation 
(they can only be prepared in the entire absence of air and water) 
characteristic of the small class of compounds of ionized carbon. 
It is only when one of the five hydrocarbon radicals is (like tri- 
phenylmethyl and benzyl) of the rare type for which lonization is 
possible 2 that compounds of this kind can be formed at all ; 
attempts to attach five methyl groups to a nitrogen atom invari- 
ably failed, since the methyl group cannot ionize. 3 

For boron we have the evidence of its compounds with ]8-di- 
ketones like acetylacetone. As we have seen (p. 120), these 
diketones form two links with the central atom, one normal and 
the other co-ordinate, and usually an atom combines with as 
many of them as it has valencies, forming twice that number of 
covalencies. Thus aluminium forms a compound 

O O 

1 Schlenck and Holtz, Bei\ 1916, 49, 603 1917, 50, 274, 276 

2 Schlenck and Holtz (Ber. 1917, 50, 262) have shown that while the alkyl 
and phenyl compounds of the alkali metals, such as NaCH 3 and NaC fl H 5 , 
are colourless substances insoluble in ether, the benzyl compounds, like 
those of tnphenylmethyl, are bright red, and give conducting solutions m 
ether. It is clear from the colour and the conductivity that the latter are 
salts containing ionized carbon, e g. Na[CH 2 C 6 H 5 ], while the former are 

3 See also Staudinger and Meyer, Helv. Chem. Ada, 1919, 2, 608. 

Relation to Periods 155 

in which it is 6-covalent . We should expect boron, as it is likewise 
trivalent, to form a similar six-covalent compound BA 3 (A being 
the univalent chelate radical). But it does not : it reacts 
with only two diketone molecules, thus becoming four-covalent, 
and gaining six more electrons (one from each of the two normal 
covalencies, and two from each of the two co-ordinate links). 
This gives it nine valency electrons, one of which is expelled, 
the complex forming a cation 



\ x*\ / 

R-C=O O=C-R 

It is difficult to see what reason there can be for this difference 
in behaviour between boron and aluminium, both of which have 
the same number of valency electrons, except that the covalency 
of boron is limited to four, while that of aluminium can rise to six. 

With lithium, beryllium, and oxygen the evidence is only 
negative, but it is fairly convincing. Beryllium, for example, 
in its salts very readily takes up four molecules of water of 
crystallization (as does lithium), but not more, forming the 
stable hydrated ion [Be, 4H 2 0] ++ , whereas magnesium in the 
same salts forms the almost equally stable hydrated ion 
[Mg, 6H 2 0] ++. 

(iii) In the next short period (sodium 11 to chlorine 17) we 
have plenty of evidence for covalencies of 6, but none for higher 
values. A covalency of 6 has been established for sodium, 1 and 
almost certainly (from the hydrated ion) for magnesium. For 
aluminium we have the acetylacetonate, for silicon the fluo- 
silicates, and for sulphur the hexafluoride. The behaviour of 
this last compound, as we shall see later (p. 158), shows that 
sulphur cannot exceed the covalency of 6. The same is shown 
for silicon by the formula of the acetylacetonate, exactly as the 
limit of 4 was established for boron : the silicon compound, 
instead of being SiA 4 , which would involve a covalency of 8, 
is [SiA 3 ]X ; as compounds of the type MA 4 are possible with 
heavier elements of the same periodic group (for example, with 
zirconium, cerium, and thorium), this must mean that the 
covalency of silicon is limited to 6. 

1 Sidgwick and Brewer, J. C. S. 1925, 127, 2879. In the corresponding 
lithium compound the metal ig*bnly 4-covalent. 

156 Covalency Maxima 

In the first long period (potassium 19 to bromine 35) there is 
abundant evidence that covalencies of 6 can occur. That higher 
covalencies are impossible is shown (apart from the negative evi- 
dence) again by the acetylacetonates. Titanium and germanium, 
like silicon, form [TiA 3 ]X and [GeA 3 ]X. Still stronger evidence 
is the behaviour of selenium hexafluoride, the stability of which 
to water proves (see p. 158) that the covalency of the selenium is 
a maxinium. We may therefore conclude that up to the end of 
the first long period the highest possible covalency is 6. 

(iv) When we come to consider covalencies of 8, it must be 
remembered that they cannot be expected to arise, even with 
atoms which are capable of exhibiting them, except under un- 
usually favourable conditions. It is only the atoms with 8 
valency electrons (ruthenium and osmium : iron is excluded as 
belonging to the first long period) that can form 8 covalencies 
directly and without co-ordination, as the elements of the 
sulphur group form 6. In the earlier groups this involves the 
borrowing of a considerable number of electrons, which causes 
instability. We might however expect to find 8-covalent atoms 
in the chelate compounds of the elements of the fourth group, 
since in these compounds, as we have seen, the covalency is 
commonly twice the group valency. Accordingly we find that 
the lightest element which is known with certainty to assume 
a covalency of 8 is zirconium. While titanium, like silicon, 
forms a salt [TiA s ]X, zirconium forms a neutral compound 
ZrA 4 . Tin also gives chelate compounds in which it is 8-cova- 
lent, though not very readily. The only known un-co-ordinated 
8-covalent compound of the type MX 8 is osmium octofluoride. 
But double salts with complex anions of this type, like Na 3 [TaF 8 ], 
are numerous among the heavier elements : they are formed by 
zirconium, niobium, molybdenum, tin, cerium, tantalum, tung- 
sten, thallium, lead, thorium, and uranium. There are no certain 
instances of such anions being formed by elements lighter than 

These conclusions are supported by other lines of evidence. One 
of them is the behaviour of the simple halides of the elements 
with water. 1 If a halide, which may be represented by the symbol 
XC1, is treated with water, one of four things may happen. 

(1) It may ionize : 

_XC1 > -X + + Cl- 

as with lithium, beryllium, sodium, magnesium, aluminium, &c. 
1 Sidgwick, J. C. S. 1924, 125, 2672. 

Action of Water on Halides 157 

(2) It may hydrolyze (more or less completely) into the 
hydroxide and hydrochloric acid : 

-XC1 + H 2 O -- > -X-OH + HC1 
as with the chlorides of boron, silicon, phosphorus, sulphur, &c. 

(8) No reaction may take place, as with carbon tetrachloride 
and sulphur hexafluoride. 

(4) It may hydrolyze in another way, not replacing the halo- 
gen by hydroxyl but by hydrogen, with the formation of hypo- 
chlorous acid : 

-XC1 + H 2 - * -X-H + HOC1. 

This occurs with nitrogen chloride (and the organic substituted 
nitrogen chlorides) and with chlorine monoxide OCl a . 

(1) The limitation of this first process, that of ionization, has 
already been discussed in the light of Fajans' theory. The 
electrovalency will tend to pass into a covalency as the positive 
charge on the ion increases, but will do so less readily as the ion 
grows larger. Hence it is only in the earlier periodic groups that 
ionization of the halides occurs, and it extends to more highly 
charged ions as we reach the later periods. 

(2) When ionization does not occur, we have the possibility 
of the water attaching itself to the molecule and reacting with 
the halogen. Now water is active both as donor and as acceptor : 
an atom which can increase its valency group can co-ordinate 


with the oxygen X^-O^ and one which is able to lend a 

pair of electrons with the hydrogen X-s>-H-O-H. In boron 
trichloride, for example, the boron has a sextet, and so is a ready 
acceptor : it forms a link with the oxygen, giving 


and a chlorine atom is then eliminated with a hydrogen from 
the water, leaving a hydroxyl group attached to the boron : 
by a repetition of this process the chloride is hydrolyzed to 
boric acid. The same happens with silicon tetrachloride, 
because although the octet of the silicon is complete, it can 
expand to twelve. It happens also with phosphorus trichloride 
and pentachloride, and with most the halides of the heavier 
elements when they do not ionize. 

(3) The position of carbon tetrachloride is different. The 
octet of the carbon is not only complete, but (unlike that of the 

158 Covalency Matcima 

silicon in silicon tetrachloride) is incapable of further expansion. 
The carbon is neither an acceptor nor a donor : it cannot ui any 
way attach itself to the water. Hence no reaction occurs at all : 
the indifference of carbon tetrachloride even to strong alkali is 
well known, and the halogens in substituted hydrocarbons are 
scarcely attacked by water. To find similar inactivity where 
the covalency limit is six, we must go to the hexahalides of the 
sixth group, such as sulphur hexafluonde. Here again we have 
a completely shared valency group of the maximum size, and 
no reaction occurs. The inactivity of sulphur hexafluoride is its 
most marked characteristic : it is not attacked even by fused 
sodium. Selenium hexafluoride is equally inactive, and this is 
strong evidence that a covalency of eight does not begin until 
after selenium. On the other hand, tellurium hexafluoride, 
although in the pure state (for example, in its volatility and 
stability to heat) it closely resembles the hexafluorides of 
sulphur and selenium, differs sharply from them in being at 
once hydrolyzed by water, giving telluric acid. This shows that 
the valency group is not of the maximum size, and that in 
tellurium (second long period) a covalency of eight is possible. 
The other hexahalides of this and later periods MoF fl , WF 6 , 
WC1 6 , UT 6 are likewise hydrolyzed by water. It is remarkable 
that the same is true of osmium octofluoride, which is perhaps 
an indication that a covalency of ten is possible for osmium. 

(4) Nitrogen chloride (and also chlorine monoxide) is in a 
different position again. The octet of the nitrogen is complete 
and cannot expand, but it is not wholly shared. It has a lone 
pair of electrons, and so can co-ordinate as a donor with the 
water, giving 


The nitrogen having attached itself to the hydrogen of the water 
remains combined with it, while the hydroxyl comes away with 
a chlorine atom as hypochlorous acid. 1 Chlorine monoxide 
hydrolyses in the same way to two molecules of hypochlorous 
acid : it thus fits in with the scheme, though it cannot be said 
to lend it much support, as it is difficult to see how the reaction 
could go any other way. 

1 This explanation of the very peculiar hydrolysis of chlorine covalently 
attached to nitrogen seems more probable than the hypothesis that such 
compounds contain a new kind of ' positive ' chlorine. 

Silicon and Carbon Chains 159 

It is thus possible to account, on the basis of this limitation 
of the maximum covalency, for all the methods of reaction, or 
non-reaction, of the simple halides in presence of water. 

Many other peculiarities of the periodic table can be explained 
in the same way. It has been pointed out by G. N. Lewis and 
others that many elements in the second short period differ 
markedly from the corresponding members of the first period in 
their strong tendency to polymerize. This is obvious if we con- 
trast carbon dioxide and carbonic acid with silicon dioxide and 
silicic acid, or N 2 and O 2 with P 4 and S 8 . Lewis explains this 
by the assumption that the formation of double bonds is possible 
(or at any rate easy) only for elements in the first period. But 
apart from these facts there is no reason for making such an 
assumption, and there are many compounds of the heavier ele- 
ments whose properties are not easily explicable unless we 
assume the presence in them of double bonds. A more probable 
explanation is the difference in the covalency maximum. The 
carbon in carbon dioxide has fully satisfied both its valency and 
its covalency : its octet is complete and incapable of expansion. 
But an atom from the second period which has completed its 
octet (like the silicon in SiO 2 ) still has the power of forming two 
more covalencies by co-ordination, and hence the molecule can 

Another example is the contrast in stability between chains 
of carbon atoms and chains of silicon atoms. Saturated hydro- 
carbon chains, as -CH 2 -CH 2 -, are of course unattacked by water 
either alone or in presence of acid or alkali. But their silicon 
analogues react quantitatively to give the silicoethers and 
hydrogen : 

_^i_^i_ + H 2 O = -^i-O-Si- + H 2 . 

a reaction which has been used by Kipping to estimate the 
number of Si Si links in the molecule of a compound. This is 
clearly due to the power of silicon (but not carbon) to act as an 
acceptor by increasing its valency group : 

HO-SiR 8 

H\ - 

It is particularly to be noticed that this reaction is very highly 
catalysed by alkalis, that is, by hydroxyl ion. This ion, being 
negatively charged, will be a very active donor, and will readily 

160 Covalency Maxima 

attach itself to the co-ordinately unsaturated silicon, giving the ion 
H-O->-Si<^ ; this is the anion of an excessively weak acid 

H-O->-Si<^ H, which by co-ordination with its own hydrogen ion 

passes into the neutral form g>O--Sj( , and thus the hydration is 


Another example is afforded by the volatile tetroxides M0 4 . 
These are no doubt eight-covalent, with a double link to each 
oxygen : the alternative formula, with co-ordinate links, would 
presumably be that of a less volatile compound. This requires 
that the central atom should have eight valency electrons, a 
condition fulfilled by iron, ruthenium, and osmium. Of these 
the last two form remarkably volatile tetroxides, but iron forms 
none. This must be because the covalency of iron cannot rise 
to eight, whereas that of the other two metals can. 

Many other individual cases might be quoted in support of the 
rule, some of which will be mentioned in other connexions later : 
but enough has been said to show that the evidence is strong. 

It should be noticed that there are a certain number of com- 
pounds which appear to indicate values of the covalency in 
excess of those allowed by the rule. In none of these have the 
structure and molecular weight been definitely ascertained. 
Nearly all of them are either highly complex salts, or com- 
pounds containing large numbers of molecules of water or 
ammonia. These latter will be discussed more fully when we 
come to deal with the question of solvation (Chapter XI), but it 
may be said here that they can be interpreted in three ways. 
(1) They may be crystalline aggregates of independent mole- 
cules, their stoichiometric proportions being due to the regu- 
larity of the crystalline structure : (2) the water and ammonia 
compounds may contain double molecules of these associated 
substances, such as certainly occur in liquid water, so that the 
number of covalencies of the central atom required for the 
solvation is only half the number of solvent molecules : (8) they 
may be real exceptions to the covalency rule. The most probable 
view would seem to be that adopted by Werner, that they are 
partly due to (1) and partly to (2). If they are real exceptions 
to the rule we can only say that the rule expresses the behaviour 
of the enormous majority of compounds, and that exceptions 
are rare and apparently erratic. 

Odd Covalencies 161 

It must be clearly understood that the rule only states the 
maximum number of covalencies which an atom can form under 
the most favourable conditions. The actual value even the 
highest value which a given element attains in any of its known 
compounds may and often does fall below this. It depends 
on the nature of the element in question, and on that of the 
groups with which it is combined. Fluorine, for example, pro- 
bably owing to its small size, readily forms compounds exhibiting 
the maximum covalency of other elements, as in [HFJ~, SF 6 , 
and OsF 8 . Chlorine is much less effective : no octochloride is 
known, and only one hexachloride (WC1 6 ). Again, if we con- 
sider the effect of the nature of the central atom, we find that 
in both the extreme groups I and VII, especially in I, the highest 
values seldom appear. With the alkali metals 4 is rare, and 
6 is only known in two similar compounds of sodium and 
potassium. In Group II B (Cu Ag Au) the maxima are 6, 6, 
and 8 ; but 4 is seldom exceeded. It is obvious that the accumu- 
lation of borrowed electrons which a univalent metal needs for 
a high covalency will rarely be stable. The halogens again 
give uniformly low values. Fluorine (maximum 4) seldom 
exceeds 1 and never 2 : chlorine and bromine (maximum 6) 
seldom reach and never exceed 4 : iodine (maximum 8), though 
it shows a markedly greater preference than the other halogens 
for the higher covalencies, never rises beyond 6. 

We have so far considered only the even covalencies. Odd 
covalencies are of course frequent, although less so than even ; 
but there is no indication of any limit in the periodic table to 
the odd as there is to the even : there is no sign that, for example, 
the earlier atoms of the second short period, which can exceed 

4, can rise to 5 but not to 6. The relation of an odd value to 
the next higher even value is that of unsaturation ; 1- and 
3-covalent atoms are of course familiar, as in H 2 and NH 3 ; 
but even here there is a great increase of stability as we go 
from 8 to 4, as may be seen by comparing the ease with which 
ammonia forms ammonium compounds with the much smaller 
tendency of oxygen to form oxonium salts. A covalency of 

5, though far less common than either 4 or 6, is well estab- 
lished in the fifth group, where normal 5-covalent compounds 
can be formed directly : thus we have the volatile compounds 
PF 6 (B. Pt. -75, stable up to high temperatures), AsF 6 (B. Pt. 
-58), SbCl B (B. Pt. 140), NbF 5 (B. Pt. 220), NbCl 6 (B. Pt. 
240), TaF 6 (B. Pt. 229), and TaCl 6 (B. Pt. 242), to which may 



Covalency Macoima 

be added IF B (B. Pt. 97) ; the electrical conductivities of the 
three chlorides are no greater than that of conductivity water. 1 
Covalencies of 7 are very rare, but probably occur in such com- 
pounds as K 4 [RuCl 7 ] and K 2 [TaF 7 ]. 

The relation between the covalency maximum and the struc- 
ture of the atom, about which something, but not very much, 
can be said, will be dealt with in the next chapter, after we have 
considered the method of calculating the valency groups. 

1 Holroyd (Chem. andlnd. 1923, 848 : Holroyd, Chadwick, and Mitchell, 
J. C. S. 1025, 2402) found that phosphorus pentachlonde had a small con- 
ductivity in nitrobenzene solution, although it had none in benzene or 
ethylene dibromide ; he infers the presence of an ionized form [PC1JC1. 
It is possible that in a donor solvent of fairly high dielectric capacity like 
nitrobenzene lonization may occur to a small extent, but the work is of 
a preliminary nature and needs confirmation. In the pure state there is 
no reason to doubt that phosphorus pentachlonde is covalent, like the 



relation between the nature of a valency group and its 
-- stability, and the connexion of this with the structure of 
the atom as a whole, form the most fundamental problem in the 
theory of valency, because it is on this stability that the chemical 
properties of every element depend. 

So long as we are concerned only with the isolated atoms in 
which none of the electrons are shared either the neutral 
* normal ' atom, or a monatomic ion the problem can be dealt 
with on the lines which Bohr has laid down. The fundamental 
principles have been established, and the completion of the 
details may be left to the physicist. But with atoms which are 
united by shared electrons, forming non-polar links or cova- 
lencies and these are the most interesting to the chemist 
the Bohr theory is at present quite unable to deal. We know 
that the shared electrons enter in some way into the constitution 
of both the atoms concerned, but we cannot calculate their 
orbits, or the relations of these to the orbits of the unshared 
electrons. The mathematical difficulties of this problem are so 
great that it is unlikely that the physicist will be able to make 
any great progress with it, unless the chemists to some extent 
prepare the ground, and by examining the great mass of chemical 
evidence which they have collected, discover empirically so far 
as they can what arrangements of shared and unshared electrons 
do actually occur in stable molecules. 

The first step is to determine how many electrons surround 
the nucleus of an atom in a molecule of known structure, and 
how many of these are shared with other atoms. As the number 
in a neutral isolated atom is the atomic number, that in the 
combined atom (which will obviously vary with the state of 
combination) may be called the Effective Atomic Number 
(E.A.N.). The simple rules for determining this may be re- 
peated. We have to find how the original atomic number of 
the atom in question is modified by the state of combination. 
We must therefore make the following changes in it. 

(1) For every covalency, due to the attachment of a univalent 

radical, we add 1. 

(2) For every co-ordinate valency, such as is formed by 

164 Stable Valency Groups 

attaching to the atom a complete molecule, when the 

atom acts as acceptor we add 2 : when it acts as donor, 

no change is made. 
(3) If the resulting complex is an ion, we add the value of its 

negative or subtract that of its positive electrovalency. 
These are the only rules. The following examples will make 
their application clear. 

BinK[BF 4 ] 5+4 + 1 = 10 4 

CinCH 4 6 + 4 - 10 4 

NinNH 3 7 + 3 = 10 3 

Nin[NHJCl 7 + 4-1 = 10 4 

Cl in H [>C1<] 17 + 1 - 18 4 

Co in K[Co(NH 3 ) 2 ClJ 27 + 2x2+4 + 1 - 86 6 
Co in [Co(NH 3 ) B Cl]Cl 2 27 + 2x5 + 1-2 = 36 6 

The subscript number following the E.A.N. gives the number of 
covalent links formed by the atom. This being the number of pairs 
of shared electrons, the number of unshared is the E.A.N. minus 
twice the covalency : e. g. for 36 8 it is 36 - 2 x6 = 24. 1 

Some convention must be adopted to distinguish the shared 
from the unshared electrons. This may be done by underlining 
the former (8), but as they always occur in pairs, 2 it is con- 
venient to write them as two equal numbers (4, 4), as if they 
formed two equal subgroups. 3 It must however be clearly 
understood that no assumptions are made as to the quantum 
numbers of the shared orbits (see the discussion on this point, 
p. 100). 

In this way we reach a complete determination of the numeri- 

1 In practice it will be found convenient in examining the compounds 
of a particular element to count up the ' effective valency ' or ' electronic 
increment ', which is the total change which must be made in the atomic 
number to give the E.A.N. (for the two cobaltammines above this is 9 e ) : 
this can be arrived at by inspection, and is the same for all compounds or 
the same type ; the E.A.N. is then got by adding the atomic number of 
the element. 

a The rare instances on which hydrogen atoms are attached by 1 -electron 
links (see p. 102) must be dealt with separately. 

3 The groups, subgroups, and grouplets of the unshared electrons are of 
course distinguished as before by enclosing the subgroups or grouplets of 
the same group (that is, with the same principal quantum number) in 
brackets : e. g. (2, 2, 4) for the complete second quantum group of 2 x 2 U , 
2 x 2 21 , and 4 x 2 ?2 electrons. 

Effective Atomic Number 165 

cal values of the effective atomic number, which tells us how 
many electrons the atom has in the compound, and how many 
of them are shared. If our general views of valency are correct, 
and if we have correctly interpreted the structure of the mole- 
cule, the calculation up to this point does not admit of any 

The next question is what we can do to distribute these elec- 
trons into groups in accordance with the laws which Bohr has 
shown to determine the arrangements in isolated atoms. Here 
of course we are on more uncertain ground. The only sound 
principle is to adhere as closely as we can to the physical con- 
clusions, and make no new hypotheses that we can avoid. The 
sharing of the valency electrons may be assumed to make no 
difference to the distribution of the unshared so far as the 
lowest quantum groups are concerned. These will be filled in 
the same way as in the isolated atom. For example, in K 2 [PtCl 6 ] 
the effective valency of the platinum is 8 6 , and hence its E.A.N. 
is 86 6 . Thus it has 86 2x6 = 74 unshared electrons. No one 
would dispute that 2 of these 74 are in the first quantum group, 
8 in the second, and 18 in the third : this makes 28, and leaves 
46 to be accounted for. Since the fourth quantum group of 32 
is filled up in the uncombined atom at Lu 71, it is practically 
certain that by the time we reach Pt 78, with 7 more units of 
positive charge on the nucleus, it will be too firmly fixed for the 
number of its electrons to be modified by the presence of the 
shared electrons. We may therefore assign 32 more electrons 
to this fourth group, leaving 14, of whose positions we know 
nothing except that certainly some, and very likely all, occupy 
5-quantum orbits. We can thus sum up our conclusions in the 

Pt in K 2 [PtCl 6 ] = 86 6 - (2) (8) (18) (32) (14) 6, 6. 
Potassium platinichloride is a stable compound, and so this 
must be a stable arrangement of electrons ; it is not readily 
increased by reduction or diminished by oxidation ; but whether 
this stability of the 14 unshared electrons is due to their number 
alone (together with the nuclear charge), or depends on the pre- 
sence of the 12 shared electrons 1 in other words whether we 

1 The remarkable stability of a group of 12 shared electrons of a 
covalency of 6 is already sufficiently obvious, and has been so ever since 
the early days of Werner's theory ; but we are more immediately con- 
cerned with the stability of the unshared group of 14 which is associated 
with it in compounds of this type. 

16 6 Stable Valency Groups 

should regard the (14) 6, 6 as analogous to a single Bohr group, 
or to two such groups we do not yet know, although the 
examination of the chemical evidence and comparison with the 
E.A.N.'s of this and similar elements in other compounds may 
be expected to throw light on the point. 

I have intentionally chosen a rather complicated example, and 
one in which the result has no obvious symmetry, in order to 
show that the method expresses the known facts with the mini- 
mum of assumptions. The only assumption made about the 
shared orbits is that they differ in some way from the unshared : 
their division into two equal quasi-subgroups is merely to indi- 
cate their invariable occurrence in pairs. If it is asked what 
advantage we gain by constructing these formulae the answer 
is that it is only in some such way as this that we can register 
the stable electronic constitutions of different atoms, and so 
discover how the stability is related to the structure. In the 
platimchlorides we find stable arrangement of 14 unshared 
electrons along with 12 shared. By comparison with similar 
formulae for the atoms in other compounds we may find how 
far this grouping is generally stable, and how far its occurrence 
in the platmichlorides is determined by one or other of the 
factors present in that particular type of molecule : the cova- 
lency, the nature of the attached groups, or the periodic group 
or horizontal period to which platinum belongs. We thus find, 
for example, that (with some doubtful exceptions) the 4-covalent 
platinum compounds such as K 2 [PtCl 4 ] (84 4 = (2) (8) (18) 
(32) (16) 4, 4) do not have 14 but 16 electrons in this group : 
that iridmm forms a compound K 3 [IrCle] in which it has the 
same E.A.N. as platinum in the platmichlorides, but that 
osmium does not do so : that in the next triad likewise the two 
last elements, rhodium and palladium, form similar compounds 
K 3 [RhCl 6 ] and K 2 [PdCl e ], but not ruthenium : and that in the 
first triad it is the first two elements, iron and cobalt, which 
behave in this way (as in K 4 [Fe(CN) ] and K 3 [CoCl fl ] ), and not 
the third, while chromium is remarkable for giving a series of 
complex derivatives closely related (often even in colour) to 
these cobalt compounds, such as K 3 [CrCl ], in all of which it 
has 11 electrons in the place of these 14. These examples are 
only mentioned to show that this method of formulation is of 
use in comparing in detail the properties of elements throughout 
the periodic table. 
Many examples work out more symmetrically than these, 

Effective Atomic Number 167 

especially when we are not dealing with the transition elements 
(in the wider sense). The elements of the first four periodic 
groups, in their normal compounds with the group covalency, 
all give a number of unshared electrons either equal to that of 
an inert gas (typical elements and A subgroups) or 8 less (i. e. 
with the last electron group of the inert gas removed : B sub- 
groups), and we are obviously justified in arranging these num- 
bers as in the inert gases. For example : 

12+2 = 14 2 -(2) (8) 2, 2 

BinBCLj 5+8 = 8 3 - (2) 3,3 

CinCH 4 6+4 = 10 4 =(2)4,4 

Si in Si(CH 3 ) 4 14 + 4 - 18 4 - (2) (8) 4, 4 

TiinTiCl 4 22+4 = 26 4 - (2) (8) (8) 4, 4 

Zn in Zn(C 2 H 5 ) 2 30+2 = 32 2 = (2) (8) (18) 2, 2 

In in InCl 8 49+3 = 52 3 - (2) (8) (18) (18) 8, 3 

Sn in SnCl 4 50+4 = 54 4 = (2) (8) (18) (18) 4, 4 

Pb in Pb(C 6 H 5 ) 4 82+4 - 86 4 = (60) (18) 4, 4 

(It is obviously convenient in dealing with large numbers not 
to write out the earlier groups in full every time, and, as in 
the last example, we may use the symbols (10), (28), (60) for 
the completely filled groups of the first two, three, or four 
quantum numbers.) 

At this point we may consider whether any relation can be 
found between the Bohr electronic structures and the covalency 
rule. On the Bohr system in its recently modified form, while 
the successive sizes of the groups (with the same first quantum 
number) are 2, 8, 18, 32 (2n z , where n is the first quantum 
number), those of the subgroups (with the same first and second 
ouantum numbers) are 2, 6, 10, and 14 (i. e. kn -2), and those of 
the grouplets (with all three quantum numbers the same) 2, 4, 
6, 8 (i. e . 2n) . We might expect that the number of shared electrons, 
which is twice the covalency, would follow one or other of these 
divisions, in which case the successive covalency maxima would 
be, if they corresponded to the groups, 1, 4, 9, 16 : if to the 
subgroups, 1, 8, 5, 7 : and if to the grouplets, 1, 2, 8, 4. None 
of these relations holds : on the contrary we find that the values 
of the covalency maxima themselves correspond to the sizes 
of the grouplets (2, 4, 6, 8). (This rather surprising result, that 
the number of pairs of shared electrons is to be compared with 
the number of electrons in a grouplet, is some justification for 

168 Stable Valency Groups 

writing the former as we have done in the form of two equs 
grouplets (n, ri).} In the isolated atom the grouplets of thes 
sizes form "the completion of the successive quantum group; 
and if there is a real relation between the grouplets and the cc 
valencies, this should show itself by the positions in the serie 
of elements at which the two phenomena first appear. Tha 
there is such a relation is seen if we examine the effective atomi 
numbers of a series of atoms in compounds in which they exhibi 
a high covalency, and compare them with those given by imag 
nary compounds whose formation, otherwise possible, is foi 
bidden by the covalency rule. These are shown in the followin 
table (A - the radical of acetonylacetone, C 5 H 7 O 2 ). 

I. Actual. 

H in [F-H^F] 4 2 - 2, 2 

BeinBeA 2 10 4 - (2)4,4 

CinCCl 4 10 4 - (2)4,4 

Al in A1A 3 22 6 - (2) (2, 2, 4) 6, 6 

Si in [SiA 3 ]X 22 6 - (2) (2, 2, 4) 6, 6 

S in SF 6 22 6 - (2) (2, 2, 4) 6, 6 

Ti in [TiA 3 ]X 30 6 = (2) (2, 2, 4) (2, 2, 4) 6, 6 

ZrinZrA 4 52 8 = (2) (2, 2, 4) (2, 2, 4, 4, 6) (2, 2, 4)8, \ 

II. Non-existent : forbidden by covalency rule. 
BinBA 3 14 6 - (2)6,6 

Si in SiA 4 26 8 - (2) (2, 2, 4) 8, 8 

Ti in TiA 4 34 8 ~ (2) (2, 2, 4) (2, 2, 4) 8, 8 

It is obvious that the distinction between the structures c 
the possible and those of the impossible compounds is thi 
The covalency cannot exceed by more than two the number < 
the largest (unshared) grouplet in the atom : the series of eve 
numbers which is formed by the concluding grouplets of tl 
successive quantum groups is continued by the maximui 
covalency number. Thus in compounds of hydrogen, whei 
there are no unshared electrons, the maximum covalency is 2 
in the first short period the only complete unshared group is thf 
of 2, and the maximum covalency is 4 : after neon (2) (2, 2, < 
the 4-grouplet of the second quantum group is established, an 
a covalency of 6 becomes possible. So far the new covalency lim 
always appears as soon as we should expect it, but the beginnir 
of the covalency of 8, if we have placed it correctly, is rathi 

Covalency Rule and Bohr Theory 169 

later than we should have anticipated. The 18 group, with its 
grouplet of 6, is firmly established by the time we reach zinc 
(30), and germanium (32) might form a tetra-acetylacetonate 
GeA 4 , in which it would have the structure 82 +12 = 44 8 = (2) 
(2, 2, 4) (2, 2, 4, 4, 6) 8, 8, which seems permissible. So too 
selenium in its hexafluonde SeF 6 (34 +6 = 40 6 = (2) (2, 2, 4) 
(2, 2, 4, 4, 6) 6, 6) should be capable of rising to a co valency of 
8, and hence of accepting two more pairs of shared electrons, 
in which case it would be hydrolyzed by water. The evidence, 
as we have seen, is that this germanium compound cannot be 
formed, and that selenium hexafluoride is unaffected by water, 
and so must contain selenium in its highest state of covalency. 
It follows that a covalency of 8 is not possible in the second 
half of the first long period (Cu 29 to Br 85), but only when we 
reach the second long period (after ICr 86), when we find for 
example ZrA 4 , whose E.A.N. is given in the table above. It 
would therefore seem that while covalencies of 4 and 6 become 
possible as soon as the 1- and 2-quantum groups respectively 
.are filled with unshared electrons, that of 8 cannot begin as 
soon as the 3-quantum group of 18 is full, but only when the 
atom has an unshared group of 8 in addition, or, as we probably 
should put it, when the nuclear charge is at least 8 units larger 
than corresponds to the completion of the third quantum 
group. As we shall see shortly, this is in accordance with the 
principles of the Bohr structures. 

We can therefore express the covalency rule in terms of the 
structure by saying that a covalency of 2n + 2 does not become 
possible until there are enough unshared electrons in the atom, 
to fill completely the first n quantum groups : with this further 
qualification, that covalencies of 2, 4, and 6 begin as soon as 
this condition is fulfilled, but that of 8 only some 8 places later. 1 

1 The strict application of this rule would indicate that when the fourth 
quantum group of 82, with its grouplet of 8, was completed (after lutecium 
71, at the end of the rare earth metals), a covalency of 10 would be possible, 
although to judge from the behaviour of the 8-covalent compounds we 
should expect its occurrence to be rare, and its beginning to be consider- 
ably delayed. The only definite argument in favour of its existence is the 
fact already mentioned, that osmium octofluoride is hydrolyzed by water, 
which suggests that the covalency of osmium is not limited to 8. In this 
connexion the hydrates of the acetylacetonates of zirconium, cerium, and 
hafnium, ZrA 4 , CeA 4 , and HfA 4 should be noticed. (Zr . Blitz and Clinch, 
Z. anorg. Chem. 1904, 40, 218. Ce : Job and Goissedet, C. 72. 1918, 157, 50. 
Hf : v. Hevesy and Logstrup, Ber. 1926, 59, 1890.) The zirconium and 
hafnium compounds contain 10 molecules of water, the cerium compound 

170 Pure and Mixed Valency Groups 

It is to be observed that there is a marked difference between 
the grouping of shared and unshared electrons, in that the 
former are able to form large groups with a smaller nuclear 
charge than would be required by the latter. In the Bohi 
structures grouplets of 6 do not begin until we reach copper (29), 
with a nuclear charge one unit greater than corresponds to the 
completion of the third quantum group of 18. But a covalency 
of 6 (which presumably involves something like a grouplet oi 
6 shared electrons) is found as early as aluminium (13) and even 
sodium (11), where the total number of electrons in the com- 
bined atom (E.A.N. 22 6 ) greatly exceeds the nuclear charge. 
If we suppose every shared electron to count as a half, the atom 
in both cases has the equivalent of 16 electrons 3 and 5 more 
than corresponds to its atomic number : and yet the grouping 
is stable, while a simple anion such as [Co] (E.A.N. 28 - (2) 
(8) (18) ), in which the grouplet of 6 would be completed, cannot 
exist owing to the instability of the (unshared) 18 group in so 
weak a positive field. 

As the covalency increases, the need of a greater charge on 
the nucleus seems to make itself felt : and this no doubt is the 
reason why the appearance of the covalency of 8 is delayed. 

Pure and Mixed Valency Groups 

Among the electrons of the combined atom it is convenient 
to distinguish those of the core from those of the valency group. 
The core is composed of the inner groups of unshared electrons 
which take no direct part in the chemical combination : the 

is stated to contain 11, which is within possible experimental error of 10. 
There is no question of the hydration of metallic ions, since the compounds 
are not ionized, and no other diketone derivatives containing anything 
hke this amount of water are known. These hydrates are obviously of an 
unusual type : they are formed by preparing the acetonylacetonate in 
aqueous solution, but when once the water has been removed (as by re- 
crystalhzation from absolute alcohol) it cannot be replaced. It is con- 
ceivable that the atoms of these metals, having completed their valency 
groups of 16 shared electrons by combination with the diketone radicals 
m the usual way, then form a further group of 20 by co-ordination with 10 
molecules of water : 

ZrA 4 , 10H 2 : 72 8+10 = (2) (2, 2, 4) (2, 2, 4, 4, 6) (2, 2, 4) (8, 8) (10, 10) 
CeA 4 , 10H 2 : 90 8+10 = (28) (2, 2, 4, 4, 6) (2, 2, 4) (8, 8) (10, 10) 
This suggestion, in the present state of our knowledge, does not seem very 
probable, and no parallel instances have yet been found ; but the facts are 
worth noting. 

Valency Group and Core 171 

valency group consists of all the shared electrons, and any un- 
shared which are not accommodated in the inner groups. If 
the valency group contains both kinds, shared and unshared, it 
is called mixed, if one kind only, pure. Completely unshared 
valency groups occur only in isolated atoms or monatomic ions, 
and do not concern us here, so that by pure groups we mean 
those in which all the electrons are shared. 

The methods by which we can form an idea whether all the 
unshared electrons are included in the core, or whether some of 
them form part of the valency group, are best illustrated by 
a series of examples. On the Bohr theory, as we have seen, the 
valent 1 elements fall into two classes. In the first of these 
all the quantum groups are complete 2 except the highest. This 
last is then the valency group of the isolated atom, and we may 
assume that in the formation of compounds the lower groups 
are unaffected (as regards their size) and remain filled with 
unshared electrons. They constitute an unalterable core, and the 
valency (apart from, certain limited exceptions to be considered 
later) either is constant, or changes by two units at a time owing 
to rearrangements of the valency electrons, as in the change from 
trivalent to pentavalent nitrogen. The second class of elements 
consists of those (enclosed in frames in the table, p. 39) in whose 
atoms not only the highest quantum group but also the next (in 
the rare earth metals the next two) is imperfectly filled, contain- 
ing some number intermediate between two stable values (8 and 
18, or 18 and 32). In such atoms the valency group is not fixed, 
as one or more electrons from the next incomplete group may be 
utilized for chemical combination. This leads to valencies vary- 
ing by single units, to the formation of coloured and para- 
magnetic ions, &c. These are the transition elements in the 
wider sense. 

In atoms of this last class it is difficult to tell with any cer- 
tainty what is the size of the valency group, as we do not know 
how many electrons from the next group may be drawn into it ; 

1 This convenient term may be used for those elements which exhibit 
valency, i. e. all but the inert gases. 

2 By ' complete ' is meant that they have attained a size which gives 
them great stability, not necessarily that they have reached their maxi- 
mum size of 2n 2 (where n is the principal quantum number). As we have 
seen, a group of 8 or 18 electrons has this stability, even when it can 
ultimately expand to 18 or 32 : for example, the fourth quantum group 
contains 8 electrons in krypton, 18 in xenon, and 82 in emanation. Any 
group of 8, 18, or 32 electrons may thus be called complete. 

172 Fure and Mixed Valency Groups 

but in those of the first class, with completed quantum groups, 
the electrons required to fill these inner groups cannot be called 
upon to act as valency electrons, and so the size of the core is 
fixed and known. Hence in the compounds of the first class of 
elements we can reach a definite conclusion as to whether there 
are any unshared electrons outside these inner groups, and if so, 
how they are related to the number of shared electrons. 

This may be illustrated from the elements of the second short 
period, which ranges from neon (2) (8) to argon (2) (8) (8), the 
intermediate elements having from 1 to 7 electrons in the third 
quantum group. The core of 10 electrons = (2) (8) is very 
stable, and can scarcely be broken into by any means, certainly 
not by chemical combination. So in the compounds of these 
elements we know that we have to assign 10 unshared electrons 
to the first two quantum groups, which are then full and cannot 
hold any more. Any additional unshared electrons must lie 
outside these two groups, and may be supposed to form along 
with the shared electrons a separate organization having its 
own rules of stability, the valency group. 

Of the earlier members of this period, which are metals, we 
may consider magnesium 12 - (2) (8) (2). This forms the non- 
covalent ion [Mg] ++ (if we assume it unhydrated), in which the 
two valency electrons are gone, and the core alone remains. It 
also forms di-covalent compounds such as MgEt 2 and MgEtl, 
and by co-ordination it can assume covalencies of 3, 4, and 6 : 

[Mg]++ - 12-2 - 10 = (2) (8) 

CH 3 -Mg-I 12 + 2 = 14 2 -(2) (8) 2, 2 

(C 2 H 5 ) 2 0->Mg< H 3 12+4 - 16 3 - (2) (8) 8, 8 

12 + 6 = 18 4 = (2) (8) 4, 4 

[Mg(OH 2 ) 6 ]Cl a 12 + 2x6-2 = 22 = (2) (8) 6, 6 

So with aluminium we get, amongst others, forms like these : 

[Al]+ + + 18-8 - 10 = (2) (8) 

A1(CH 3 ) 3 13+3 = 16 3 -(2) (8) 8, 8 

Na 3 [AlF 6 ] 13 + 6+8 - 22 6 - (2) (8) 6, 6 

and with silicon : 

SiH 4 14 + 4 = 18 4 - (2) (8)4, 4 

K 2 [SiF 6 ] 14 + 6+2 - 22 6 = (2) (8) 6, 6 

Octet Formation 173 

In all these examples we have found, besides the core of 10, 
nothing but shared electrons 4, 6, 8, and 12 according to the 
covalency. This is what is meant by a pure valency group. It 
is evident that with a stable core such a group is reasonably 
stable whatever its size (provided that it is even, and does not 
exceed the covalency limit for the atom), though the chemical 
behaviour shows that particular sizes such as 8 and 12 are more 
stable than 2, 4, or 6 : that is, that covalencies of 4 or 6 are 
more stable than those of 1, 2, or 8. 

The next element is phosphorus. This gives three types of 
compounds, with covalencies of 3, 4, and 5 (6 does not seem to 
have been observed), as in PH 3 , [PH 4 ]I, and PF 5 . 

PH 3 15+3 - 18 3 = (2) (8) 2, 3, 3 

[PH 4 ]I 15+4-1 = 18 4 -(2) (8)4,4 

PF 6 15+5 - 20 5 = (2)1(8)5,6 

With sulphur we find (in addition to certain anomalous com- 
pounds) covalencies of 0, 1, 2, 3, 4, and 6 : 

[S]" 16 + 2 = 18 (2) (8) (8) 

[C 2 H 6 -S]K 16 + 1+1 = ISj. = (2) (8) 6, 1, 1 

(C 2 H 5 ) 2 S 16+2 = 18, = (2) (8) 4, 2, 2 

[(C 2 H 5 ) 3 S]I 16+3-1 - 18 a -(2) (8) 2, 8, 8 

16+2 = 18 * = (*H 8 )^ 

SF 6 16 + 6 = 22 6 - (2) (8)6,6 

It will be seen that with covalencies of 4 and 5 in phosphorus, 
and of 4 and 6 in sulphur, we again get pure (wholly shared) 
valency groups ; but with those of 1, 2, and 3 we have quite 
a different arrangement, the total number of electrons outside 
the core being always 8, of which 2, 4, or 6 may be shared, the 
rest being unshared : the stability of the group seems to depend 
only on its total number. This is an example of mixed valency 
groups, and constitutes the famous octet. 1 

The octet has been so much discussed, and is found in so 
many familiar compounds, that we are inclined to regard it as 
the typical valency group, and to imagine that a group of 
valency electrons, whose stability is determined by its total 

1 In writing the E.A.N. it is convenient to include all the electrons of 
the octet in one bracket, as in (6, 1, 1), (4, 2, 2), &c. This is merely to 
simplify the counting, and does not imply the assumption of any quantum 
relation between the shared and the unshared electrons of the octet. 

174 fwre and Mixed, valency woups 

number, with little reference to whether the individual electrons 
are shared or not, is the normal state of things. The facts 
however are quite otherwise : the mixed group is rather the 
exception than the rule, even among atoms with a covalency 
less than 4. It is obvious that a mixed octet cannot occur in 
the elements of the first three periodic groups. These elements 
are limited in their valency by the number of electrons which 
they have to offer, and even by sharing all of them normally, 
and so doubling their number, they cannot form a complete 
octet, much less one in which there are unshared electrons : 
their incomplete octets are indeed unsaturated, and tend to 
complete themselves, as we have seen, by co-ordination, but in 
so doing they form not a mixed but a wholly shared group. The 
atoms might no doubt complete their octets by taking up un- 
shared electrons and so becoming anions, as in the imaginary 
compound K 2 [BC1 3 ], in which the sextet of the tri-covalent 
boron would be increased to 8 (2, 3, 3) by two electrons taken 
from the potassium, but such compounds are never formed. 
The elements of the fourth periodic group, having 4 valency 
electrons, form an octet directly, but this of course is wholly 

The mixed octet is therefore confined to the elements of 
groups V, VI, VII, and possibly VIII, and even here is not 
found, so far as can be ascertained, in the A subgroups (V, Nb, 
Ta : Cr, Mo, W, U : Mn : and the transitional triads forming 
group VTII). The size of the core in these A elements is of course 
variable, but the stable sizes for each element can be discovered 
by examining its compounds, and if the mixed octet occurred 
we ought to find that there was a tendency for the atoms, when 
their covalency was less than 4, to have a total E.A.N., irre- 
spective of the covalency, 8 units greater than a stable form of 
core. No such tendency is however observed, although a pure 
octet, that is, a covalency of 4, is common enough. 

When we come to covalencies of more than 4, we find few 
signs of any tendency for unshared electrons to form part of the 
group. Not only are the stable groups of 12 or 16 electrons 
wholly shared, but, which is very surprising, there seems to be 
no tendency * for the odd covalencies of 5 and 7, that is, groups 
of 10 and 14 shared electrons, to make themselves up to the 

1 Certain exceptions are found in which an apparently inert pair of 
valency electrons occurs ; but these, which will be discussed later, are not 
more frequent with odd than with even covalencies. 

Octet Formation 175 

apparently more stable numbers of 12 or 16 by the addition of 
a pair of unshared electrons. On the contrary the exceptional 
prevalence of a covalency of 5 in the fifth group, as in PF 6 , 
indicates that the stability of 10 shared electrons is greater when 
there are no unshared electrons present in the group with it. 

The conclusion therefore is that while purely shared groups 
of any even number from 2 to 16 are possible, a mixed group 
can only (or almost only) occur when its total number is 8, and 
even then only when it makes up the E.A.N. of the atom to 
that of an inert gas, with the result that it is confined to ele- 
ments a few places before such a gas. The great stability of the 
inert gas structures seems to make possible a co-operation of 
the shared with the unshared electrons, so that when an atom 
reaches this number it acquires a stability to some extent in- 
dependent of how many of the electrons are shared. 

The exceptional character of a group of 8 electrons is indicated 
by the remarkable stability of the wholly shared octet. Examples 
of this have already been given in the behaviour of the ammo- 
nium as compared with the oxonium compounds, in the stability 
of the ions XO 4 of the phosphates, sulphates, perchlorates, 
chromates, &c., and in the 4-covalent chelate compounds of 
sodium and thallium (p. 146). A further proof is afforded by 
the comparison of the covalent halides of the third periodic 
group with those of the typical and B elements of the fourth. 
The trihalides (with the exception of those of boron) are 
always less volatile than the heavier tetrahalides, as the following 
list of boiling-points shows : 

BC1 3 A1C1 3 FeCl 3 GaCl 3 

18 183 280 220 

CC1 4 SiCl 4 TiCl 4 GeCl 4 SnCl 4 PbCl 4 

78 58 186 86-5 114 (M.Pt.-16) 

The difference is due to association of the trichlorides (those of 
aluminium, iron, and gallium have been shown to give double 
molecules in the vapour), while the tetrahalides show no sign 
of association. It is evident that the trivalent elements, having 
incomplete octets, strive to complete them by co-ordination, 
the metal acting as acceptor and the halogen as donor : thus 
A1 2 C1 6 is presumably 

CL Cl 



176 The Atomic Core 

The tetrahalides might behave in the same way, since (with the 
exception of carbon) the elements can assume a covalency higher 
than 4 : but the covalency of 4 is so stable that this does not 
happen. 1 

The presence of this group (4, 4) is no doubt an important 
factor in the stability of the carbon compounds, and explains 
why carbon can scarcely be induced to form an anion [CR 3 ]~, in 
which the octet, though it would still be complete, would not 
be fully shared. 

The Atomic Core 

Having seen what are the stable forms of the valency group 
we have next to consider the core ; for it is these two factors 
which between them determine the stability of the combined 
atom, and so that of the whole molecule. Among the transition 
elements in the wider sense, where several different cores are 
possible for the same element, this is a very complicated ques- 
tion, and is better discussed in connexion with the individual 
elements. But even here we can see the importance of the core 
in determining the state of the atom. With iron, for example, 
we find two states of the core running through the whole of the 
compounds, from the simple ions to the most highly covalent 
derivatives : in one of these the core is composed of 24 and in 
the other of 28 electrons : 

Fe : 26 - (2) (8) (14) (2) 
Ferrous : Fe++ : 24 = (2) (8) (14) 

K 4 [Fe(CN) 6 ] : 26 +6 +4 = 36 6 - (2) (8) (14) 6, 6 
Ferric : Fe+ + + : 23 - (2) (8) (18) 

K 3 [Fe(CN) 6 ] : 26 +6 +3 - 35 6 - (2) (8) (13) 6, 6 

In the same way we find among the compounds of copper the 
cuprous core of 28 - (2) (8) (18) and the cupric of 27 - (2) (8) 
(17). The current terminology of these complex compounds, in 
which this difference of core is recognized (under the name of 
a difference of valency) as the basis of the classification of the 
compounds of a given element, shows how useful the distinction 
is. The numerical value of the valency is on this system the 
difference between the number of electrons in the core and the 
number in the isolated atom. 2 

1 The remarkably low volatility of zirconium tetrachlonde, which boils 
at a red heat, may possibly be due to a polymerization of this kind. 

a It should be noticed that certain modifications of structure which are 
often difficult to determine m practice leave the core unaffected. A co- 

Variable Valency with fixed Core 177 

Among the elements less far removed from (usually not more 
than 6 places before or 3 after) the inert gases, more definite 
conclusions can be reached. The core is normally composed of 
complete groups, and its number is that of an inert gas or 8 less 
(0, 2, 10, 18, 28, 86, 46, 78, 86). The maintenance of a fixed 
core is however compatible with certain changes of valency in 
the ordinary sense of that term, many of which have already 
been pointed out. The core of the nitrogen atom is 2 in ammonia 
and in the ammonium ion : that of silicon is 10 in the tetra- 
halides and in the fluosilicates : that of sulphur is 10 in diethyl 

Ft T^t 

sulphide -g.^S, in diethyl sulphoxide )>S--O, and in diethyl 

sulphone EK *O 

and that of chlorine 10 in ethyl chloride Et-Cl, in chlorous acid 
H-0 C1->O, in chloric acid H-O-C1^ O , and in perchloric acid 

H-O\ -0 


c/ x o 

It will be noticed that on the old conception of valency, in 
which no distinction was made between covalency and electro- 
valency, and the co-ordinate link to oxygen was written as a 
double bond, all these changes require an alteration of the 
valency by an even number : thus in the above examples the 
valency of nitrogen changes from 3 to 5, that of silicon from 
4 to 8 (if the fluosilicate is regarded as a true complex salt), 
that of sulphur from 2 to 4 and 6, and that of chlorine from 1 to 
3, 5, and 7. All these changes involve the formation of co- 
ordinate links ; but there is another series (also without altera- 
tion of core) arising through the possibility of the mixed octet. 

ordinate link in which the atom acts as acceptor has no effect : the core 
is the same in the simple and in the dimeric form of aluminium chloride, 
and indeed the same also in the aluminium ion, whether it is hydrated or 
not. Again in double salts it is often impossible to be certain whether the 
components really form a complex molecule, or only a crystalline aggre- 
gate ; but this does not affect the size of the core, which is the same, for 
example, m PbCl 4 , as it is in K 2 [PbCl fl ]. Also the doubt whether, say, an 
oxygen atom is united by a double link or a co-ordinate link (for example, 
in trimethylamine oxide) is unimportant from this point of view : the core 
is 2 both in R g N = O and in R 3 N--O. These differences all affect the 
covalency, but not the core. 

3o6s A a 

178 The Atomic Core 

The elements of the later groups may, if the covalency rule 
permits, use all their valency electrons for the formation of 
a number of normal covalencies equal to the group-number, as 
in PF 5 and SF 6 . But if they form mixed octets, then* valencies 
instead of being n (group-number) are 8 n (in groups V, VT S 
and VII 8, 2, and 1) : here again the difference (n (8 n) =*> 
2n -8) is necessarily an even number. 

But of the observed changes of valency in these elements SL 
considerable number involve a real alteration of the core, nearly 
always (apart from copper and gold, where the instability of the 
core has already been explained) in the direction of an increase, 
there being more unshared electrons in the atom than we shoulcl 
expect. Some of these are isolated instances, which are better- 
discussed under the elements in question, as in the ' odd mole- 
cules ' NO, CIO 2 , and InCl 2 . Others again throw little light on. 
the stability of atomic structures, because the properties of the 
molecules in which they occur show that these structures are 
in fact highly unstable : as in the compounds of trivaleirb 
carbon, to which those of divalent nitrogen and univalerrb 
oxygen may now be added. 1 These may be called ' forced * 
valencies : they indicate an unstable electronic grouping whicti. 
rearranges itself as soon as it has an opportunity of doing so. 
There is however one considerable class of abnormal valencies 
which can be recognized as being due to some common cause, 
that, namely, in which two of the valency electrons appear to 
have become inert, as though they had been absorbed into the 
core. This phenomenon is first to be noticed in group III B in 
InCl, and more markedly in the thallous compounds : in the 
typical and B elements of group IV it is especially prominent, 
from the divalent compounds of carbon to those of germanium ., 
tin, and lead. In group V B we find it in antimony and still 
more in bismuth, in VI B in sulphur, selenium, and tellurium., 
and in VII B in iodine and bromine and possibly in chlorine. 
Thus it is most marked in the fourth group, and is generally- 
prevalent among the heavier B elements. It is especially evi- 
dent in the series of elements following gold : mercury, thallium, 
lead, and bismuth. The new development of the Bohr theory 
due to Stoner and Main Smith indicates a possible reason for 
this peculiarity. We now realize that the first two electrons in. 
any group, forming the grouplet N n , correspond to the pair of 
l n electrons in helium, and can have a certain completeness of 
1 Perhaps chlorine dioxide should be included under this head. 

The Inert Pair of Electrons 179 

their own, approaching that which they have in helium, where 
they form a complete group. We might thus anticipate that 
under some conditions the first two valency electrons of an 
element could become more like core-electrons, and refuse either 
to ionize, or to form covalencies, or both. 1 How their presence 
in this state would react on the rest of the valency group 
whether they would have to be counted as part of it, or would 
change the conditions of its stability, or finally should be re- 
garded as having no connexion with it and genuinely forming 
a separate group of the core cannot at present be predicted ; 
but something may be learnt by examining the chemical facts. 
Why this inertness of the N 1]L pair should appear precisely where 
it does in the periodic table, we cannot say : the spectral evi- 
dence supports the chemical, but no reason has been assigned 
for either. The property shows a singular development in the 
successive elements mercury, thallium, lead, and bismuth, with 
the structures : 

Orbits . 5 6 1X 6 2 

Hg 80 = (60) (18) 2 

Tl 81 = (60) (18) 2 1 

Pb 82 = (60) (18) 2 2 

Bi 83 = (60) (18) 2 3 

The normal valencies should of course be mercury 2 : thallium 3 : 
lead 4 : bismuth 5, or in octet formation 3. The actual valencies 
in the salts appear to be mercury 1 and 2, thallium 1 and 8, 
lead 2, and bismuth 8 in each case less, and in all but that of 
mercury 2 less, than we should expect : two of the valency 
electrons seem to be under some conditions capable of remaining 
unshared and unionized. But a closer inspection shows that 
there is a remarkable change in the character of the inertness. 
In the earlier members of the series the 6 n pair can be shared 
although they 'cannot, or can only with difficulty, be ionized. 
Mercurous mercury is not really univalent. The ion, as has been 
abundantly proved, is not [Hg] + but [Hg 2 ] ++ : each atom is 
using both of its valency electrons, but one is shared with the 
other atom giving [Hg -Hg] + + , the E. A.N. of the atom thus being 

80 + 1-1 = 80i - (60) (18) 1, 1. 
The strong tendency for these electrons to serve rather for 

1 See Grimm and Sommerfeld, Z. /. Phys. 1920, 36, 36 but many of 
their examples of change of valency are of the kind which have been 
explained above without assuming a change of core. 

180 The Atomic Core 

covalencies than for electrovalencies is shown by their being able to 
link the two metallic atoms together, a structure which is almost 
unique. That this tendency extends to both the valency electrons 
of the mercury is proved by the very small lonization of mercuric 
salts, 1 which, on the principles we have already accepted, indicates 
that the equilibrium in the reaction HgX 2 ^ [Hg]X 2 is very far 
on the left-hand side. The small iomzatioii of the mercuric salts, 
together with their slight tendency to complex formation, points 
to a further peculiarity presumably due to the same cause as 
the inertness of the N n pair. The mercury in the covalent 
compound X Hg X (as in the chloride or cyanide) has only 
a quartet of shared electrons, which in this element seems to 
be quite stable, although it would normally be highly un- 
saturated : compare for example the very unstable ZnEt 2 with 
the stable HgEt 2 . A somewhat similar peculiarity occurs in the 
compounds of divalent carbon, in which the E.A.N. is (2) 
(2 S 2, 2) : these are far less unsaturated than we should expect 
from the extraordinarily strong tendency of the carbon to main- 
tain its octet : the recently discovered methylene diacetal 2 
Et-O-C-O-Et (B. Pt. 77 : vapour density normal) is not 
attacked by bromine, and only slowly by alkaline permanganate. 
It is to be noticed that by the time we reach lead, the stability 
of this (2, 2, 2) group has disappeared : the simple covalent 
compounds always have a complete shared octet. 

The same inertness is shown even more strongly by thallium, 
where we have the thallous ion T1+ - 80 - (60) (18) 2 : 
this has been shown to be partly polymerized like the mercurous 
ion to [T1J++, presumably [T1=T1]+ + , in which one of the 
three electrons of each atom is ionized, and the other two are 
shared. The univalency is almost limited to the ion and the 
liquid aUcylates such as Tl 0-Et, where we have the E.A.N. 
82J - (60) (18) (2) 1, 1 : the compounds of higher covalency 
(2, 8, 4, and 6) nearly always involve the use of all three electrons, 
having E.A.N.'s of the form (60) (18) n, n. It is remarkable 
that although thallium readily forms alkyl~derivatives of great 
stability, nbne are known of the types TIAlk or Tl(Alk) 3 : they 
are all salts of the type [Tl(Alk) 2 ]X, with a quartet of shared 
electrons as in the mercury alkyls. 

1 The mercuric salts of organic acids are as a rule ionized to about the 
same extent as the acids from which they are derived : the halides of course 
much less. 

2 Scheibler, Ber. 1920, 59, 1022. 

The Inert Pair of Electrons 181 

Lead shows this peculiarity in its most marked form : it is 
divalent in all its simple salts, and quadrivalent in all its stable 
alkyl and aryl compounds : 

[Pb]Cl a 82 -2 - 80 - (60) (18) 2 
Pb(CH 3 ) 4 82 +4 - 86 4 - (60) (18) 4, 4 

So it appears that of the 4 electrons outside the stable core of 
78 two alone can be removed by ionization, while all 4 are avail- 
able for conversion into covalencies. 

In bismuth two of the 5 electrons outside the core seem to 
have become inert for nearly all purposes. Except in a few 
organic derivatives bismuth never attains a valency of more 
than 3. Since the majority of the familiar bismuth compounds 
are tri-covalent, it might be argued that this is merely an 
example of the formation of a mixed octet (2, 3, 3), and this 
may perhaps be true of the tri-covalent compounds themselves : 
but no similar explanation can be given of the appearance of 
this pair of unshared electrons in derivatives in which the 
bismuth has covalencies of 4, 5, and 6, as may be seen by com- 
paring the following effective atomic numbers : 

[PHJI 15 +4 -1 - 18 4 = (2) (8) 4, 4 

K[Bi(S0 4 ) 2 ] 88+4+1 - 88 4 - (60) (18) 2, 4, 4 

SbCl 5 51 +5 - 56 5 - (28) (18) 5, 5 

K 2 [BiCl 5 ] 88 +5 +2 - 90 5 = (60) (18) 2, 5, 5 

Even among the tri-covalent compounds such as the tri- 
halides there is a marked difference in behaviour between those 
of bismuth and those of the lighter elements of the subgroup 
such as phosphorus and arsenic. The former have much more 
the character of salts of a [Bi] +++ ion 80 - (60) (18) 2. They 
form a series of double salts with the halides of the more electro- 
positive metals (such as that given above), and bismuth can re- 
place the metals of group III A (lanthanum and the rare earth 
metals) in the peculiar double nitrates M" 3 [M'" (NO 3 ) 6 ], 24H 3 0. 
Both these properties are characteristic of elements with only 
three valency electrons. 

Thus it appears that in the series of elements from mercury (80) 
to bismuth (83) the N^ electrons of the valency group first 
become reluctant to ionize, and finally will scarcely function as 
valency electrons at all. The further discussion of the peculiari- 
ties of this grouplet must be left until we come to deal with 
individual elements. 

18 2 Absolute Valency 

Definition of Absolute Valency 

We have so far been engaged in disentangling the different 
forms of valency, in discovering their electronic mechanism, and 
m discussing the conditions of their formation. We can now 
describe the state of a combined atom in terms of its electro- 
valency, its normal covalency, and its co-ordination. It is worth 
considering what remains of valency in the older sense as repre- 
senting a state of the atom giving it a definite power of chemical 
combination. Can we speak absolutely of the valency of an 
atom in a compound, and if so, how can we define it m terms 
of the electronic structure ? No completely satisfactory answer 
can be given to this question. The modem distinction of 
different types of valency shows that the combining power of 
an atom may be due to more than one cause and may arise in 
more than one way, and it is not possible to express all the 
variations of this power as numerical values of a single con- 
stant. This is largely due to the complications introduced by 
the existence of mixed valency groups. On the whole the best 
definition of absolute valency seems to be that adopted by 
Grimm and Sommerfeld, 1 that it is numerically equal to the 
number of electrons of the atom ' engaged ' (beansprucht) in 
attaching the other atoms. It is thus equal to the difference 
between the atomic number and the number of unshared elec- 
trons in the combined atom., 

In atoms with pure valency groups, the unshared electrons 
constitute the core ; the valency is then the difference between 
the atomic number and the size of the core (with iron (26), for 
example, it is two for compounds with a ferrous core of 24, and 
three for those with a ferric core of 23) ; we thus retain the 
familiar terminology, and at the same time relate it to the 
electronic structure. In the simple anions the difference between 
the number of electrons before and after combination is nega- 
tive : a fluorine atom with 9 unshared electrons becomes an ion 
[F]~ with 10, and has a valency of 1. The definition will thus 
cover these atoms also. With octet formation it can still be 
applied ; it gives the same values of the valency as the older 
formulae, and like them it fails to distinguish the co-ordinate 
link from the true double link : thus in 

H-0 X *0 

H-cr ) 

1 Loc. cit., p. 44 

Absolute Valency 183 

since 6 electrons of the sulphur are engaged 1 (one to each 
hydroxyl and two for each co-ordinate link), the valency is 6, as 
it was in the older symbol 2 



This method of designating the valency in octet compounds 
(2 for sulphur in H 2 S, 6 in H 2 SO 4 ), though familiar, involves 
abandoning for them the idea of the importance of the core, 
which only contains those electrons not counted towards the 
octet, and is the same (10), for example, in sulphur whether four 
(H 2 S) or 8 (H 2 SO 4 ) of the octet electrons are shared. 

This definition gives a definitely wrong result when applied to 
such a molecule as the hydroxyl ion, in which an atom forms 
a covalency, and also receives an electron as an anion. Here the 
oxygen gams one of the two electrons it needs for the octet 
directly, and the other by sharing the electron of the hydrogen, 
to which it lends one of its own. Thus the number of its unshared 
electrons is the same as in the isolated atom, and so on the 
definition we have adopted its valency should be zero. 

In general then it may be said that if a definition of absolute 
valency is needed, the best that can be given is that it is equal 
to the change in the number of unshared electrons caused by 
the combination. This leads in the majority of compounds to 
the numerical values to which we are accustomed, but in a few 
it breaks down entirely, while in most of those containing a 
mixed octet it fails to indicate the more important differences 
which the electronic theory detects. Where however the atom 
has a pure valency group, this definition expresses the changes 
in the core, which are the really fundamental characteristics of 
the atomic structure. 

In order to show the results to which this definition leads, a 
series of values of the valency deduced from it may be given : 

Hydrogen 1 in H-CH 3 and [F-Ek-F]" : boron 8 in BF 3 and 
K[BFJ : aluminium 3 in [Al]+++, [Al, 6H 2 O]+++ A1(CH 3 ) 3 , 

1 The same is of course true of the ion Q^S^Q : here the sulphur 

also has 8 shared electrons, but has received two of these as its anionic 
charge, so that it is using 6 of those which it had originally. 

2 The difference between the links S--O and S = O is that while m 
both two electrons from the sulphur are shared by the oxygen, in the latter 
two additional electrons from the oxygen are also shared by the sulphur. 


Absolute Valency 

and A1 2 C1 8 : silicon 4 in SiCl 4 and K 2 [SiF 6 ] : lead 2 in [Pb]Cl 2 , 
4 in Pb(CH 3 ) 4 and K 2 [PbCl e ] : nitrogen & in NH 3 , 5 in 

[NH 4 ]I and CH 3 -N^ : oxygen zero in [H-0]~ and [CH 3 -O]", 

2 in [O]" and Et 2 O, 4 in [Et 2 OH]Cl : sulphur 2 in [S]~ and 
Et 2 S, 4 in Et a S-*O, 6 in H 2 S0 4 and SF 6 : iodine 1 in [If 


and I-CH 3 , 3 in C 6 H 6 -I<^J and [(C 6 H 5 ) 2 I]N0 3 , 5 in IF 6 , and 
7 in (HO) 5 I-*O. 

xi .. ^ LIBRARY 


1 ' * x- ' _ 

AN important group of co-ordination compounds consists oT^ 
_A_ those which are formed by solutes with solvents. So far 
as the solutes are purely covalent, their solvation products do 
not call for special discussion ; but the combination of ionized 
molecules with solvents, and especially with water, is so frequent 
as to need further consideration : hydrated salts are the most 
familiar instances of co-ordination compounds in the whole of 
chemistry. Other hydroxylic solvents behave in the same way 
as water, and so also do ammonia and its substitution products, as 
was pointed out by Werner. 1 We have an immense amount of 
data as to the composition of the solids which are obtained from 
such solutions, and their study should be of great value in extend- 
ing our knowledge of the factors which determine co-ordination. 
There are, however, as we shall see, considerable difficulties in 
interpreting these data, which in the present state of our know- 
ledge can be only partially overcome. The most serious of these 
is the doubt whether all the solvent molecules which appear m 
the formula really form part of the molecular complex. 2 

If our theories of valency are true, they ought to be applicable 
to every kind of molecule. We have abandoned the idea of mole- 
cular compounds, and concluded that the forces which hold the 
constituent atoms of a molecule together must either be electro- 
valencies or covalencies ; and we have found these sufficient to 
account for all those molecules whose size can be definitely 
determined, either in the gaseous state or in solution. Now 
among the large number of recorded comp6unds of which the 
molecular weight cannot be determined, a considerable propor- 
tion are only known to exist from the facts that a solid phase 
can be produced which contains the elements in a proportion 
corresponding to a possible formula, and that this proportion is 
independent of changes (within certain limits) of the conditions 
of separation. The evidence for the existence of salt hydrates 

1 Z. anorg. Chcm. 1893, 3, 267. 

2 Another question is how far we can have double (polymerized) solvent 
molecules, each attached to the ion only by a single covalency : this will 
be discussed later (Excessive Hydration, p. 198). 

3fe B b 

186 Salvation 

is invariably of this kind : we cannot, as will be shown later, 1 
determine the degree of hydration in solution, and we commonly 
assume that if a solid hydrate of a particular formula separates, 
this hydrate also exists as a molecule (or as the ions of a molecule) 
in solution. The same applies to the compounds with ammonia 
which separate from the solution of a salt in liquid ammonia, or 
are formed by the absorption of ammonia gas. Again, we have 
numerous double salts, undoubtedly forming solid phases of 
definite formula, which nevertheless give no indication of their 
existence in solution. How far are we justified in assuming that 
such compounds have any existence as single molecules that 
all the constituent atoms are held together by covalencies or 
electrovalencies ? If we could be sure of it, our task would be 
considerably simplified. We should know that we had to frame 
our rules so as to include the constitution of all substances which 
can be obtained in the solid state with a definite composition 
expressible by a formula : we should have to find places in our 
scheme for all the molecules of water in every known hydrated 
salt. On the other hand we should have to abandon all ideas of 
a covalency limit, and to admit that many atoms can, under 
certain apparently quite erratic conditions, expand their valency 
groups to an almost indefinite extent. But it seems very doubt- 
ful whether such a conclusion is justified. We know from X-ray 
measurements that the crystal unit often contains two or more 
molecules : in many instances there is no probability that these 
molecules can combine chemically ; they are packed together 
in the crystal owing to the operation of forces altogether sub- 
ordinate to those which unite the atoms in a molecule, these 
being no doubt due to the weak external fields which surround 
every atom. If the crystal structure is destroyed by fusion or 
solution, these molecules separate again. No one would maintain 
that structural chemistry ought to be able to provide valency 
links between such molecules for example, between the two 
benzene molecules in the crystal unit of solid benzene. But if 
similar molecules can be held together in the crystal in this way 
without chemical linkage, why not also dissimilar molecules ? 
It seems quite possible that when a substance separates from 
a solvent, the crystal unit may contain one or more molecules 
of the solvent along with a molecule of the solute, without there 
being any closer union among these molecules than there is 
between those of benzene in the crystal unit of solid benzene. 

1 See p. 190. 

. , Definition of Molecules 187 


This view is supported by the existence of hydrates of substances 
which can scarcely be supposed to be capable of forming a chemi- 
cal union with the water. Crystalline hydrates have been shown 
to be formed not only by the halogen derivatives of the paraffins, 
such as methyl and ethyl chlorides, bromides, and iodides, 
methylene and ethylene chlorides, and chloroform, 1 but also by 
methane itself, 2 and even most conclusive of all by the inert 
gases. 3 Most of these contain 6 molecules of water to one of 
solute. Their melting-points usually lie near 0, and when the 
solute is a gas their dissociation pressures are high, and they are 
only formed under pressure. The hydrates of the inert gases 
have the following dissociation pressures at : xenon 1-15 
atmospheres, krypton 14 5, argon 98 5. It is very difficult to 
believe that these are real chemical compounds ; it seems much 
more probable that the components are held together only by the 
crystalline forces : the open structure of ice no doubt facilitates 
the production of such aggregates. 

Werner certainly thought that water molecules could exist in 
this form in a crystal. He definitely assigns a position of co- 
ordination (which we should call covalency) to some of the water 
molecules in certain hydrates, whilst he assumes that others 
have no part in the molecular structure. He often took pains to 
get experimental evidence of this difference of function, by 
showing that one part of the water could be removed much more 
easily than the rest, or without such changes in the molecule as 
further dehydration produced. Biltz has expressed the same 
view with respect to ammonia. Some compounds are known 
with enormous numbers (over twenty) of molecules of water or 
ammonia of crystallization in the formula. We must either 
suppose that the ordinary rules of covalency maxima, which 
apply to the great majority of compounds, break down com- 
pletely in a few cases, or that molecules can coexist in stoichio- 
metric proportions in the solid phase which are not attached to 
one another by definite links. There is indeed an alternative 
way of explaining these exceptional substances, which is avail- 
able when they are compounds with associated solvents, such 
as water or ammonia ; and that is to suppose that the solvent 
molecules are not each separately attached to the central atom, 

1 de Forcrand, C. R. 1880, 90, 1491 : 1888, 106, 1357 : Villard, Ann. 
Chim. 1897 [7] 11, 877. 

2 de Forcrand, C. R. 1902, 135, 959. 

3 Id., ibid., 1925, 181, 15. 

188 Salvation 

but are joined to one another in sets of two or more. The un- 
doubted occurrence in water of polymerized molecules, such 


as H 4 O 2 , having the structure H-0-H-0( H , in which the 

oxygen can still act as a donor, and the possibility (though there 
is less evidence of this) of a similar polymerization of ammonia, 
make this suggestion not impossible. The occurrence of double 
water molecules in hydrated salts was accepted by Werner, and 
is supported by the fact that in a large proportion of the salts 
which contain an excessive number of water molecules, this 
number is 8 or 12. 1 But this explanation cannot be used to 
overcome the similar difficulty which arises with a large number 
of double salts. While many of these undoubtedly form complex 
ions, sometimes of great stability (e. g. ferrocyanides, argenti- 
cyanides, &c.), there are many others which give no evidence of 
their existence except in the solid state ; and we may well 
imagine that in some the components do not actually combine 
(in the sense of forming valencies), but that all that happens is 
that the two kinds of molecules pack together into the crystal 
more easily than either kind separately. This would account 
for the existence of such salts as K 15 TaF 20 , which, if it is formu- 
lated as a true complex salt K 15 [TaF 20 ], involves the assump- 
tion of a covalency of twenty for tantalum (normal maximum 
eight), but which may really consist of, say, one molecule of 
K 3 [TaF 8 ] and twelve of KF, forming separate molecules but 
a single crystal unit. Similar considerations apply to better 
known types of double salts, such as the alums M'M'" (SO 4 ) 2 , 
12H 2 0, which cannot be shown to have any existence outside 
the solid state. 

It seems therefore that we have to bear in mind the possibility 
that the formula of a solid, where it cannot be confirmed by the 
properties of the substance in the dissolved or vapour state, may 
not represent a single molecule, but a crystalline aggregate of 
separate molecules. This inevitably introduces an element of 
uncertainty into any discussion of the structure of such com- 
pounds, which the X-ray analysis of crystals has not yet re- 
moved, although we may hope that it will ultimately do so. We 
may however provisionally assume that such complications are 
rare, and that in the majority of solvated compounds each 
solvent molecule is attached separately to some atom in the 
solute. We may begin by considering the case of hydrated salts. 
1 See below, p. 199. 

Hydration 189 


Since we know that salts are in general ionized even in the 
solid state, each water molecule must be assumed to be attached 
by means of a co-ordinate link either to the positive or to the 
negative ion. It is important to observe that a water molecule 
can be co-ordinated to another atom in two ways either by the 
oxygen of the water acting as a donor, or by the hydrogen acting 
as an acceptor : 

or X-^H-O-H. 

The general evidence indicates that, other things being equal, the 
oxygen is more likely to form the link than the hydrogen : it 
is more powerful as a donor than hydrogen as an acceptor. But 
the electrical condition of the ion X will have an important and 
possibly a deciding influence. As we have seen, the formation 
of a co-ordinate link must give something of a positive charge 
to the donor, and something of a negative charge to the acceptor, 
since the two electrons which previously belonged to the donor 
alone are now shared between it and the acceptor. In conse- 
quence, the atom is more likely to act as a donor when it is 
negatively charged, and as an acceptor when it is positively 
charged, for in this way the electrostatic equilibrium tends to be 
restored. This means that cations will act as acceptors and form 
co-ordinate links with the oxygen of the water, while anions 
will attach themselves to the hydrogen : 

There is thus a possibility of the hydration of both cations and 
anions, but from the greater co-ordinating power of the oxygen 
in water we should expect cations to hydrate more easily than 
anions. The presence of an electric charge, especially a positive one, 
will obviously promote co-ordination, so that we can understand 
why salts as a class have a stronger tendency to be hydrated 
than non-polar substances. The limit of the hydration of both 
kinds of ions is of course fixed by the covalency maximum. 

These remarks apply to the hydration of salts both in solution 
and in the solid state, but the nature of the evidence available 
for the two classes of phenomena is very different. The hydra- 
tion of ions in solution has been investigated by means of a great 
variety of physical properties, such as the density, viscosity, 
freezing-point, electrical conductivity, electrolytic transport, and 

190 Hydration 

the effect of neutral salts on solubility (' salting out ') and on the 
activity and catalytic power of hydrogen ion, as well as in other 
ways. The experimental evidence is thus extensive enough, but 
it is very indecisive. Any one who examines the voluminous 
literature 1 of the subject will, I think, conclude that there is 
good reason to believe that many ions are hydrated in water, and 
some evidence as to which ions are more hydrated and which 
less, but that we can form no quantitative idea of the number of 
water molecules combined in solution with any particular ion. 
Different methods of investigation often put a series of ions in 
the same order, but they differ enormously sometimes by a 
factor of twenty as to the absolute magnitude of the hydration. 
This is no doubt partly due to the uncertainty of the theoretical 
basis of many of the methods of calculation adopted, but there 
is a fundamental difficulty in the way of all of them. The free 
water molecules behave as electrical dipoles, and hence become 
oriented in the field of an ion. This means that in addition to any 
molecules which maybe chemically united to the ion, there will be 
a layer of molecules affected by its field, and for many purposes 
indistinguishable from those which are chemically combined. 
This applies especially to arguments based on ionic mobility, 
and on the electrolytic transport of water. The orientation of 
the dipoles in the neighbourhood of a moving ion will exert a 
drag upon it and diminish its mobility, and at the same time this 
will cause a movement of these unattached water molecules in 
the direction in which the ion is travelling. Further complica- 
tions in these electrolytic methods of determining hydration 
have been pointed out by Lindemann, 2 who shows that the 
direct impact of the ions on the water molecules will have a 
similar effect, both on the mobility and on the transport, the 
magnitude of which will depend on the mass of the ion. 

The recent developments of the theory of strong electrolytes, 
due mainly to Debye and Hiickel, while of great importance in 
themselves, do not at present give us much help towards the 
solution of the problem before us. From the point of view of 
the general theory of electrolytes, it is essential to determine the 
relation of the physical properties of the solvent to its influence 
on the activity and mobility of the ions : it is. a relatively unim- 
portant question how far this is due to the actual linkage of the 
solvent molecules to the ions. As the theory develops further, 

1 For summaries see Dhar, Z.f. Elektrochem. 1914, 20, 57 : Fricke, ibid., 
1922, 28, 161. 2 Z. phys. Chem. 1924, 110, 394. 

Solid Hydrates 191 


especially in its extensions to weaker electrolytes, and to solvents 
of lower dielectric capacity than water, we may expect the selec- 
tive effect of the true chemical links to become more prominent. 

The evidence for the hydration of salts in solution is thus too 
indefinite to be of much use to us. For the hydration of salts 
in the crystalline state the evidence is definite (and extensive) 
enough, but it needs some care in its interpretation. If we dis- 
regard for the moment the possible presence of water molecules 
which are part of the crystal unit but not of the complex mole- 
cule, it is still clear that the amount of combined water in the 
crystal need not be the same as in solution, and that in fact it 
will often be less. The powerful electrical forces between the 
opposite ions in the solid may overcome the attachment of the 
water molecules, and eliminate some or all of them. The water 
of crystallization of a salt is not determined solely by the 
tendency of the individual ions to combine with water, although 
this must at least be an important factor. While the amount 
of water combined with an ion in solution will be independent 
of the other ion present, in the crystal the number of water mole- 
cules may be the sum of those combined with the two ions in 
solution, or a smaller number : and whether it is less, and if so 
how much less, will depend on both the ions of the salt. Various 
attempts have been made to attack the problem from the 
physical side, but their success is inevitably limited. They are 
necessarily based on spatial considerations, and on the assump- 
tion that the forces between the atoms in a molecule are purely 
electrostatic and obey Coulomb's law, and they cannot (at 
present) take account of the quantum effects which must largely 
determine the stability of covalent linkages. They do, however, 
show clearly the importance of Fajans' theory * that the tendency 
of an ion to form a covalent link (in this case a co-ordinate link 
with the oxygen or the hydrogen of the water) is greater (1) the 
larger its charge, (2) the less its size if it is a cation, and (8) the 
greater its size if it is an anion. 

In spite of all these difficulties, the study of the composition 
of hydrated salts leads to interesting conclusions. A valuable 
discussion of the subject, with a detailed summary of much of 
the evidence, has been given by Lembert. 2 There are a certain 
number of salts with polyatomic ions, in which the water forms 
part of a recognized co-ordination complex, as in [Cr(H 2 0) 4 Cl 2 ]Cl 
or K 2 [Cr(H 2 O)F B ]. It is evident that in such complexes, which 
1 See p. 104. 2 Z. phys. Chem. 1923, 104, 101. 

192 Hydration 

are of great stability, the co-ordination is through the oxygen as 
donor, whether the complex is positive or negative. But setting 
these aside, it is clear that the degree cxf Ihiydration depends much 
more on the cation than on the anion. To take some of the more 
conspicuous examples, salts of lithium, beryllium, and calcium 
are nearly always hydrated : those of potassium, caesium, silver, 
mercury, and ammonium are usually anhydrous. This suggests 
that the hydration of anions is of comparatively rare occurrence, 1 
which, as we have seen, is to be expected from the fact that the 
oxygen in water has a much stronger tendency to form co-ordi- 
nate links than the hydrogen. 

We may therefore consider the following points : (1) the hydra- 
tion of cations, (2) that of anions, (3) the mutual effect of cation 
and anion in determining the degree of hydration of the solid 
salt, and (4) the instances of a greater degree of hydration than 
appears compatible with the covalency rule. 

1. Hydration of Cations 

The first point to notice is that, as Fajans' theory requires, 
the hydration increases with the electrovalency ; it is weak with 
univalent metals, stronger with divalent, and stronger still with 
trivalent : compare, for example, the series CsCl, anhydrous : 
BaCl 2 , 1 and 2 H 2 : LaCl 3 , 6 and 7 H 2 O. With the exception 
of lithium and sodium, all the univalent metals arc almost 
invariably anhydrous in their salts : K, Rb, Cs, Ag, Au', Tl'. 
The second point is that in any given periodic group the tendency 
to hydration is strongest in the lightest members, and diminishes 
as the atomic number increases : this again is in accordance with 
Fajans' theory, since the lightest ions are also the smallest. It 
is always very strong in the first two periods, and overcomes the 
first-mentioned tendency in the alkali metals lithium and sodium. 
It is particularly strong in the two metals of the first short period, 
in spite of the fact that the hydration is here limited to four : 
lithium salts are more uniformly and on the average more highly 
hydrated than those of sodium. In the case of beryllium, which 
is at once small and divalent, the firmness with which the ion 
adheres to four molecules of water is so great that the amount 
of water of crystallization in a beryllium compound can be used 
as evidence of the presence or absence of beryllium ion. Practi- 

1 This of course refers to the crystal : it is possible that anions are 
hydrated in solution, but that the linkage is not strong enough to resist the 
action of the cation in the solid. 

Hydration of Cations 198 


cally all the simple beryllium salts (chloride, sulphate, per- 
chlorate, &c.) crystallize "with four molecules of water, which 
are often very difficult to remove. The fact that the acetyl- 
acetonate and the so-called basic acetate Be 4 O(O-CO CH 3 ) e are 
anhydrous, strongly supports the other evidence that in these 
compounds the beryllium is four-covalent, and not ionized. The 
double potassium sulphate K 2 [Be(SO 4 ) 2 ] has only two molecules 
of water : this indicates that it is a true complex salt, and 
contains no beryllium ion : the two water molecules are no doubt 
attached to the SO 4 groups, which, as we shall see, can be shown 
to have a tendency to hydrate. The oxalate, which has the 
composition BeC 2 O 4 , 3H 2 O, shows by its behaviour 1 (for 
example by its great solubility) that it is not a normal salt ; it is 
certainly complex, and should probably be writtenBe[Be(C 2 4 ) a ], 
6H 2 O, having four of the water molecules attached to the 
beryllium ion, and the other two- to the oxalate groups, of the 
hydration of which there is plenty of other evidence. 

In the second member of the second group, magnesium, there 
is a very strong tendency (not quite so strong as with the 
smaller beryllium ion) for the hydration to proceed to the limit, 
which is here six. 

Of the salts of the other polyvalent metals there is little to 
remark beyond the frequent occurrence of salts with six mole- 
cules of water : Werner, 2 in establishing the existence of the 
co-ordination number six, produced fifty-one examples of such 
salts. The general diminution of hydration with the heavier 
metals (owing to increasing ionic size) prevents the co valency of 
eight from being at all widely represented. 

There are two cations which call for special treatment, hydro- 
gen and ammonium (including the substituted ammoniums). 
There is clear evidence that the hydrogen ion can take up one 
or two molecules of water, the latter representing its covalency 
maximum. Practically all the ordinary strong inorganic acids 
(for example, hydrofluoric, hydrochloric, hydrobromic, hydriodic, 
nitric, perchloric, sulphuric, selenic) crystallize with water, 
usually with two molecules (sometimes more) per hydrogen ion. 
Werner 3 enumerates thirty-three complex halogen acids such 
as ZnCl 2 ,HCl,2H 2 O, that is [H(H 2 O) 2 ]ZnCl 3 ('double salts' 
of simple halogen acids with the halides of Zn, Cu, Cd, Sn, Hg, 
Sb, Bi, Fe, Au, Ir, Pt, Ag, Te), of which all but four contain at 

1 Sidgwick and Lewis, J. C S. 1926, 1287, 2538 

2 Z. anorg. Chcm. 1893, 3, 267. 3 Neuerc Anschauungen, p. 103. 

3 6s C C 

194 Hydration 

least 2H 2 for every hydrogen ion. The hydrated ion would 
be written 

On the Fajans theory the hydrogen ion, from its minute size, 
should co-ordinate with extreme ease. It is doubtful how far the 
unsolvated ion can exist in associated solvents at all : it is not im- 
probable that the effect of such solvents in causing the ionization 
of acids is directly due to their combination with the hydrogen ion. 
The abnormal mobility of hydrogen ion (which is found in other 
solvents as well as in water) is no proof that it is not hydrated ; 
it is generally attributed to ' Grotthus conductivity ', and one 
would imagine that this could occur as easily with the solvated ion. 
Salts of ammonium and the substituted ammoniums are almost 
invariably anhydrous. This is to be expected, since in ammon- 
ium the nitrogen is covalently saturated, and the hydrogen 
attached to it can only act as an acceptor under very exceptional 
circumstances. 1 None of its salts with simple monobasic acids 
are hydrated, and when we find that the ammonium salt of a 
dibasic acid is hydrated, we may take this as evidence of the 
hydration of the anion. This is confirmed, as Lembert has shown, 
by the fact that the same acids usually form hydrated potassium 
salts, although of course potassium salts as a rule are anhydrous. 
He gives the following table to show the extent of the hydration : 






Acid Oxalate 

&> 1 

Sulphite . 
lodate . 









(Tetrasulphide 8) 




2. Hydration of Anions 

This is on the whole exceptional, but it is well established in 
certain instances. The most important is that of the sulphate 
ion. The occurrence of hydrates with an odd number of mole- 
cules of water, which as a rule is rare, is almost universal among 

1 See p. 98. 

Hydration of Anions 195 

the sulphates. We have Li 2 SO 4 , 1H 2 O and Na 2 SO 4 , 7H 2 : the 
divalent metals (Mg, Zn, Cd, Co", Ni, Mn", Cr", V") give the well- 
known series of the vitriols, of the general formula M"S0 4 , 
7H 2 O, which may be written [M(H 2 O) 6 ] (SO 4 , HaO). 1 Among 
the sulphates of the trivalent metals we find those of Al, In, 
Fe"', Ce'", and La with 9H 2 O. A similar example is CuSO 4 , 5H a O, 
the hydration of the cupric ion being usually limited to four. 
This tendency of the SO 4 ion to take up water is presumably due 
to the fact that by so doing (since owing to its negative charge 
it must attach itself to the hydrogen and not to the oxygen of 
the water) it can form the stable six-ring 

There is some evidence that the nitrate ion also can take up 
one molecule of water to form a similar six-ring 



but the behaviour of nitrates in solution is in many ways ab- 
normal: there are indications that they undergo polymerization. 2 
The oxalate ion is normally hydrated, especially in the double 
oxalates. It is found generally among organic compounds, 
whether they are ions or not, that the C=O group takes up a 
molecule of water readily whenever the next carbon atom is 
attached to negative groups, and especially when the next group 
is another carbonyl : this may be unconnected with co-ordina- 
tion, and due to the conversion of C=O into C(OH) 2 . Thus 
glyoxylic acid crystallizes with one molecule of water, oxalic 
with two, mesoxalic with one, which is retained in its esters, 
diketosuccinic with two as dihydroxytartaric, and chloral with 
one, the structures of these hydrates being presumably 

CH(OH) 2 -CO 2 H : C(OH) 3 -C(OH) 3 : CO 2 R C(OH) 2 -C0 2 R : 
CO 2 H-C(OH) 2 C(OH) 2 CO 2 H: CC1 3 CH(OH) 2 . * 

Hydroxyl also appears to take up one molecule of water : all 
the alkaline hydroxides and thallous hydroxide form mono- 
hydrates, often of great stability, though at lower temperatures 
higher hydrates are also found. 

1 The vitriols are remarkable for giving a series of double salts with the 
alkali metals and ammonium of the general form M' 2 SO 4 , M"SO 4 , 6H 2 O, in 
which one molecule of water appears to be replaced by one of the alkaline 
sulphate, a type which it is not easy to explain 2 See below, p. 198. 

196 Hydration 

Fluorides almost invariably contain water of crystallization, 
even when the cation is one which is not normally hydrated, as 
in KF, 2H 2 O and AgF, 2 and 4H 2 0. This seems to prove that 
the fluorine ion is itself capable of hydration. The behaviour 
~of fluorine is in many ways difficult to explain. On the one hand 
it should, according to the Fajans theory, as an anion of small 
size, pass less readily than the other halogens from the ionized 
to the covalent state ; and the properties of such fluorides as 
those of aluminium and tin x support this view. On the other 
hand, it has a far greater power than the other halogens of bring- 
ing out the highest covalency of an atom, as is shown in H 2 F 2 , 
SF 8 , OsF 8 , &c. This unexpected hydration of fluorine ion may 
be due to the stability of its co-ordinate link with di-covalent 
hydrogen, [F-*H-0-H]~ being analogous to [F-*-H-F]~. There 
are indications of the hydration of the ions of the other 
halogens, especially when the cation is unusually large, 2 but 
they are much less marked than with fluorine. 

3. Mutual Influence of Cation and Anion 

When the hydrated ions separate from the solution, the forces 
which they exert on one another in the solid will sometimes be 
sufficient to expel some or all of the combined water molecules. 
Fajans has suggested 8 that there is a kind of competition between 
the ions for the water, which is more likely to be retained if the 
affinity of one ion for it greatly exceeds that of the other. The 
facts certainly seem to favour this view. Since the chief factor 
in determining the affinity is the magnitude of the ionic charge, 
we should, on this hypothesis, expect those salts in which the 
ions have the same valency to be less often hydrated than those 
in which the valencies are different. Lembert finds for a large 
number of soluble salts of the ordinary strong inorganic acids the 
following statistical results : 

Valency Total Number Per cent, 

cation : anion Salts Hydrated Hydrated 

11 16 4 25 
22 8 1 13 

12 5 5 100 
21 19 15 79 
31 14 12 80 
42 10 9 90 

The distinction is very marked. 

1 See p. 88. a See below, p. 197. 3 Naturw. 1921, 9, 729. 

Mutual Effect of Ions 197 

There are also signs that a large difference in size between the 
ions has a tendency to promote hydration, quite apart from the 
requirements of the Fajans theory. This may be one reason why 
fluorine ion can take up water when it is combined with large 
univalent (and therefore unhydrated) ions such as potassium or 
silver. The metallic salts of complex acids are usually highly 
hydrated unless the cations are exceptionally large. Ephraim 
has observed with the ammonia compounds * (and there are 
indications of the same tendency with the hydrates) that the 
salts of very large organic anions, such as those of the aromatic 
sulphonic acids, have an unusual power of taking up molecules 
of the solvent. This might be explained by supposing that in 
such cases the extra molecules are merely attached by the 
crystalline forces, and not by true covalencies. 

There is one fact bearing on the relation between hydration 
in solution and hydration in the solid state which may be men- 
tioned here. The effect of different salts of the same ionic type 
(for example, salts of univalent cations and anions) at a given 
concentration on the vapour pressure of water varies over a large 
range with the nature of the salt. This can be measured by 
means of the freezing-points, which are the temperatures at 
which the solutions in question have the same vapour pressure as 
ice. The observed differences can scarcely be due to differences 
in activity or apparent dissociation, if we confine our comparison 
to strong electrolytes ; but they may well be due to the removal 
of solvent by combination with the ions of the salt. Hence, 
though our uncertainty as to the precise laws which hold in com- 
paratively strong solutions prevents us from estimating quanti- 
tatively the degree of hydration, we may fairly conclude that 
a salt which produces a larger depression of the freezing-point 
at a given concentration is more hydrated than one which pro- 
duces a smaller depression. 

We may compare with one another in this way the salts 
formed by the alkali metals, silver, and ammonium with the 
ordinary strong acids such as nitric, sulphuric, perchloric, and the 
halogen acids, and the alkaline hydroxides, at a concentration 
of six molecules per cent, (about 8-normal). 2 The depression 
calculated according to the dilute solution laws for a * completely 
dissociated ' binary salt at this concentration is 12-4. The 
observed values are somewhat remarkable. All the nitrates 

1 Ber. 1918, 51, 644 : 1920, 53, 549 : see also Biltz, Z. /. Eleklrochem. 
1920, 26, 374. a Sidgwick and Ewbank, J. C. S. 1924, 125, 2273. 

198 Hydration 

except lithium nitrate, which is the only one of these nitrates 
hydrated in the solid state, give abnormally small depressions 
(9-3 to 6-2): this is evidence of that polymerization of the 
nitrate ion which has already been mentioned. The nitrites 
behave in the same way. Setting the salts of these two acids 
aside, we find that the rest can be divided sharply into two classes 
those which form solid hydrates and those which do not. The 
first class invariably give a larger depression than the second, with 
the single exception of lithium hydroxide (hydrated), where the 
difference however is small. The highest value for any non- 
hydrated salt is 12 8 (potassium iodide) : the rest range between 
this and 10 8. The lowest value for any hydrated salt other 
than lithium hydroxide (11-6) is 18 1 (sodium chloride), and the 
values rise to 23-0 (lithium iodide). The mean depression at 
this concentration is for the thirteen salts examined which form 
no hydrates 11-5, and for the ten which form hydrates 16-6. 
The strong acids hydrochloric, hydrobromic, hydriodic, and per- 
chloric, all of which form solid hydrates, give large depressions 
from 16 1 to 28-2 : that given by nitric acid, which also forms 
a hydrate, but is probably associated to some extent in solution, 
and possibly partly non-ionized, is 14-8. 

The most surprising result of this comparison is the exact 
correspondence between the effect of the salt in solution and its 
power of forming solid hydrates. We should have expected the 
power of forming solid hydrates to depend not merely on the 
extent of hydration in solution, but also on the solubility of the 
hydrate ; it appears however that this is not so. 

4. Excessive Hydration 

The great majority of salts do not contain more water than 
is compatible with the covalency rule, if we allow for the hydra- 
tion of certain anions, where it is supported by other evidence, 
as in the vitriols, where we have reason to believe that one of 
the seven molecules of water is attached to the SO 4 , leaving only 
the normal six for the cation (beryllium does not form a vitriol). 
But there are a considerable number of salts which contain more 
water molecules than can be accounted for in this way. We may 
of course abandon the covalency rule, and admit the existence 
of co-ordination numbers of eight and twelve throughout the 
whole table, as Pfenfer does ; but we have so much evidence 
for the rule that it seems preferable to adopt one of two alterna- 

Excessive Hydration 199 

tive hypotheses, either the possibility of double water molecules, 
or that of crystalline aggregates composed of two or more mole- 
cules. It is quite possible that both hypotheses are true in 
different cases : this certainly was Werner's view. At any rate 
there is a good deal to be said for the theory of double molecules, 
which, in view of the undoubted existence of polymerized mole- 
cules in water itself, is not intrinsically improbable. The strong- 
est evidence in its favour is the fact that in a great majority of 
the salts with large numbers of water molecules the number is 
exactly twice what we should expect on the ordinary theory ; 
when the necessary allowance is made for the hydration, if any, 
of the anion we nearly always find either eight or twelve molecules 
for every cation, just as in ordinary hydrates we commonly find 
four or six. To secure this result it is sometimes necessary to 
assign a water molecule to an anion which is not usually hydrated ; 
but the fact that this assumption, which can be defended on the 
ground of the exceptional size of the cation, so often reduces the 
number of molecules remaining to eight or twelve is itself re- 
markable. Some of the more important examples 1 may be 
given : first of salts which contain exactly eight or twelve mole- 
cules of water to every cation, and then of others which contain 
these numbers in addition to one water molecule per anion. 
Salts with eight molecules of water to each cation : 

[Be, 8H 2 O] PtCl fl . 

[Mg, 8H 2 0] C1 2 : I 2 : BiCl 5 . 

[Ca, 8H 2 O] PtCl 6 : O 2 . 

[Sr, 8H 2 0] (OH) 2 : 2 : BiCl 5 , 

Salts with 12 H 2 O to each cation : 

[Mg, 12H 2 0] C1 2 : Br 2 : PtCl 6 : SO d : (C1O 3 ) 2 . 

[Ca, 12H 2 0]-C1 2 : (IO 3 ) 2 : PtBr 6 . 

[Zn, 12H 2 0] (C10 3 ) 2 : (Br0 3 ) 2 . 

[Co, 12H 2 0] C1 2 : (C10 3 ) 2 : S 2 O 3 : BiCl 5 . 

Examples of salts which may be assumed to have eight or 
twelve molecules of water to each cation if we assign one H 2 
to each anion are : 

[Mg, 8H 2 0] (Br, H 2 O) 2 : (I, H 2 O) 2 . 

[Al, 12H 2 0] 2 (S0 4 , H 2 0) 3 . 

It will be noticed that in these salts the cations are di- or tri- 
valent atoms not of very high atomic number and the anions 

1 See Lembert, I. c. 

200 Ammonia of Crystallization 

predominantly polyatomic : also that beryllium (covalency 
maximum four) rises to 8H 2 O but not to 12. 

We may conclude that the occurrence of double water mole- 
cules attached by single covalencies to the cation is at least 


The combination of ammonia with salts, like that of water, 
must be due to co-ordination : but the acceptor properties of 
the hydrogen are so much weaker in ammonia than in water 
that we should expect that the linkage would always take place 
through the nitrogen, and hence that as a rule the cation would 
be solvated but not the anion. The compounds may be divided 
according to their mode of production into two classes those 
which are formed in aqueous solution, such as the ammines of 
Werner, and those which are only formed in the absence of water, 
by the use of gaseous or liquid ammonia. The former must have 
great stability, since the ammonia competes successfully in their 
formation with a large excess of water. The strong affinity for 
ammonia shown in the formation of these ammines is peculiar 
to certain parts of the periodic table, especially the transition 
elements in the wider sense (including copper) : among these it 
seems to be strongest (in the first long period) in chromium and 
cobalt, less strong in copper (cupric), and still less in nickel and 
iron. The strength of the affinity in these ammines is shown by 
the fact that the ammonia will remain combined (through the 
nitrogen) with a negatively charged complex, as in K[Pt(NH 3 )Cl 6 ]. 

Under more favourable conditions m the absence of water, 
especially at low temperatures or in presence of liquid ammonia 
addition takes place much more easily ; salts will combine 
with ammonia at least as readily as with water. The stable 
ammines of Werner, which in presence of water are limited in 
composition by the ordinary rules of covalency, can in the dry 
state and with liquid ammonia take up sometimes as many as 
ten more molecules of the latter. 1 These extra molecules are 
far more loosely combined : they are easily removed without 
causing any fundamental change in the compound, and without 
any great change in the characteristic colour. Their position 
clearly corresponds to that of the extra water molecules in 
excessive hydration. The readiness with which they are absorbed 
increases with the electrovalency of the cation of the ammine. 
1 Ephraun, Z. anorg. Chem. 1925, 147, 24. 

Ammonia of Crystallization 201 

The general question of the combination of dry salts with 
ammonia has been investigated by Biltz and his collaborators 
in a series of papers x dealing especially with the halides of the 
uni- and divalent metals. These can absorb up to, in many 
cases, ten or even twelve molecules of ammonia per molecule of 
salt. The method of investigation was to determine at a series 
of temperatures down to the freezing-point of ammonia (-78) 
the relation between the composition and the dissociation ten- 
sion : the defimteness of the solid phases was proved by the con- 
stancy of the tension with change of composition. From the 
change of this pressure with temperature Biltz calculates the 
heat of formation of the compound from the salt and ammonia. 
The number of ammonia molecules frequently exceeds the 
covalency limit of the cation (solvation of the anion is not pro- 
bable), and although with some of these highly solvated com- 
pounds the vapour pressure is scarcely less than that of liquid 
ammonia, this is by no means always the case : thus calcium 
chloride (limit six) forms CaCl 2 , 8NH 3 , with a dissociation tension 
of 100 mm. at 2 (that of liquid ammonia is 100 mm. at 67). 
Biltz considers that in these highest ammines the later molecules 
are attached by a different kind of linkage from the earlier, and 
this is confirmed in the case of the alkaline halides by the marked 
fall m the heat of addition of ammonia after the first three or four 
molecules. 2 We may suppose either that the later additions 
go to form double ammonia molecules, or, since there is much 
less evidence of the polymerization of ammonia than of that of 
water, that they form part of the crystal unit but not of the 
complex molecule. 

The general relations between the affinity for ammonia and the 
charge and size of the cation are much the same as for water : 
the affinity is greater the greater the charge, and (m any parti- 1 
cular group) the smaller the ion, as Fajans' theory requires. 

The heat values (Q) calculated by Biltz from the change of 
dissociation tension with temperature are the partial heats of 
formation from the simple salt and gaseous ammonia : they in- 
clude the difference between the lattice energy of the ammoniate 

1 Biltz has collected and summarized the results in Z. anorg. Chem. 1923, 
130, 93. For further work see Biltz and others, ibid., 1925, 148, 145-216. 

8 Another example is beryllium chloride. The covalency limit for beryl- 
lium is 4. The compound BeCl 2 ,4NH 3 is extraordinarily stable. Its 
dissociation tension is 100 mm. at about + 200, while those of BeCl 2 , 
8NH 3 and BeCl 2 ,12NH 3 reach 100 mm. at - 49 and - 66 respectively. 

202 Ammonia of Crystallization 

and that of the original salt. This question has been discussed 
by Biltz and Grimm. 1 The lattice energy of a salt is the differ- 
ence between the energy of the fully ionized vapour and that of 
the solid salt. For an ammoniate it is equal to the heat (A) 
evolved when m gram-molecules of ammonia combine with one 
gram-molecule of the cation in the vapour, together with that 
(B m ) evolved when the ions recombine and condense to the solid 
ammoniate. Thus if Q is Biltz's value of the partial heat of 
formation, and U is the lattice energy of the original salt (which 
has been calculated by Grimm by the method of Born), then 

Lattice energy of ammoniate => A + B m = U + Q. 
This gives a more satisfactory method of comparing the affinities 
than the partial heats of formation of Biltz. From a study of 
the results so obtained, Biltz and Grimm arrive at the following 
conclusions : 

1. For the same number of molecules of ammonia the lattice 
energy falls with increasing radius of the cation (Na>Rb, 
Mg>Ba, Cu'> Ag) and also of the anion (C1>I), when the ion 
has the same number of electrons (eight or eighteen) in the outer 
(highest quantum) group. (Mercuric salts come out of place in 
this series : they should fall below cadmium, but are actually 
nearly as high as zinc ; this may be due to complications caused 
by the presence of mercurous ions.) 

2. A cation with an outer group of 18 or 20 (Pb") electrons 
gives a higher value than one in the same period with 8(Cu'>K 
Zn>Ca, Pb>Ba). 

3. For cations with the same outer electronic group, the 
lattice energy for any given number of molecules of ammonia 
is greater the greater the electrovalency. 

4. The differences between the lattice energies with the same 
cation and the same number of ammonia molecules, but a dif- 
ferent halogen, fall with an increase in the ammonia content 
when the cation has eight outer electrons, but rise when it has 
eighteen or twenty. 

It will be seen that these conclusions are in agreement with the 
Fajans theory so far as concerns the effect of charge and size of 
the cation, which alone is solvated. It should, however be 
noticed that most of these compounds are known only in' the 
solid state. There is always a possibility that some of them may 
be compounds not of the ions but of the undissociated (covalent) 

1 Z. anorg. Chem. 1925, 146, 63. 

Influence of Cation and Anion 


halide. This seems particularly likely with the cuprous and 
silver halides ; they combine with -, 1, 1|, 2, and SNH 3 , and 
both the low limit of solvation and the presence of half mole- 
cules of ammonia suggest that the halide is polymerized. 

Combination with solvents other than water or ammonia 
especially with organic substances containing hydroxyl or amino- 
groups is frequently observed ; it appears to follow the same 
general lines as the formation of hydrates and ammines, but to 
diminish in extent as the molecular weight of the solvent 




IT has been recognized since the time of Oersted and Ampere 
that magnetism is a property of electricity in motion. Every 
electric current is surrounded by lines of magnetic force, and 
every closed circuit is equivalent to a magnet of definite moment. 
It was suggested by Amp&re that a substance like iron owed its 
magnetic properties to a continuous circulation of electricity 
in its molecules, and that its magnetization consisted in the 
orientation of these circuits in the same direction. Now that 
we know that every atom contains electric charges in rapid 
motion in closed orbits, the origin of the magnetic properties of 
matter seems clear. 2 At the same time the relation of the 
magnetic properties of atoms and molecules to their structure 
is not yet fully understood. Both on the theoretical and on the 
practical side there are great difficulties to be overcome. The 
recent developments in the physical theory of the atom, and 
especially the introduction of the third quantum number, which 
has a close relation to the magnetic behaviour, have led to great 
progress, and have brought the magnetic into relation with the 
spectroscopic theory ; but it cannot be said that any completely 
satisfactory theory of atomic and molecular magnetism has yet 
been proposed. The results which have already been obtained 
are however of great interest. 

As Faraday showed in 1845, substances can be divided as 
regards their behaviour in a magnetic field into two classes those 
which tend to set themselves parallel to the field (paramagnetic) 
and those which set themselves transversely (diamagnetic). 
Paramagnetic phenomena are now divided into two sections 
those of paramagnetism proper and those of ferromagnetism. 

1 See Stoner, Magnetism and Atomic Structure, 1926 : Andrade, Structure 
of the Atom, 3rd Edition, 1927, Chapter XVI : Gerlach, Malerie, Elektn- 
zitdt, Energie, Leipzig, 1926, Chapter VIII. 

2 The magnetic field near the nucleus of an atom is of enormous intensity : 
within the K ring it is even in so small an atom as neon about 10 8 and m 
uranium about 10 11 gauss. Macroscopically the most intense permanent 
fields attainable m the laboratory are between 10 4 and 10 6 gauss, but for 
periods of the order of 1/100 second a field approaching 10 gauss might 
be produced. 

Principles of Magnetism 205 

This latter, which is distinguished by the great intensity of the 
^ forces concerned and by the occurrence of a lag in the relation 
between the state of the substance and that of the field (hysteresis 
and permanent magnetism), is confined to a comparatively small 
number of metals and a few of their compounds : though in 
general due to the same cause as paramagnetism it is clearly 
related to the structure of the solid and is not an atomic property, 
since certain alloys composed of metals with very small indi- 
vidual susceptibilities (the Heusler bronzes, for example an alloy 
of 10 per cent, aluminium, 20 per cent, manganese, and 70 
per cent, copper) have ferromagnetic properties approaching 
those of iron. Ferromagnetism, being a special case of para- 
magnetism, will therefore not be discussed further. Both dia- 
magnetism and paramagnetism are observed with matter in 
every state of aggregation, and therefore are properties of the 
\ atoms or molecules. 

Tne fundamental characteristics of dia- and paramagnetism 
were established experimentally by P. Curie, who formulated 
the two laws that diamagnetic susceptibility is independent of 
temperature, and paramagnetic inversely proportional to the 
absolute temperature. To both these laws, and especially to 
the second, there are many exceptions, which is to be expected 
since the magnetic properties of the atom are certainly affected 
by its state of combination, which will often vary with the 
temperature. In the absence of such chemical changes the laws 
may be presumed to hold. 

v The foundation of the modern electronic theory of magnetism 

was laid by Langevin in 1905 : regarding the effects as due to 
the rotating electrons, he gave a theoretical basis to Curie's laws. 
Every electronic orbit must have a magnetic moment, but by 
a suitable arrangement of their axes these may neutralize one 
another ; the simplest arrangement would be one in which all 
the orbits occurred in parallel pairs, with the two electrons of 
each pair revolving in opposite directions. In that case the 
resulting moment of the atom is zero, but it can be shown that 
the establishment of an external field will so modify the orbits 
as to produce a diamagnetic effect, which will be independent of 
the temperature and state of aggregation of the substance. This 
diamagnetic effect is common to all matter, whether it is para- 
magnetic or not. 

If the orbital moments do not neutralize one another, the 
atom is paramagnetic, and this will mask the diamagnetism. In 

206 Atomic and Molecular Magnetism 

the presence of an external field such atoms will tend to arrange 
themselves with their magnetic axes parallel to the field. This 
orientation will be opposed by the disturbing effect of their 
thermal agitation, so that unless the field is very powerful it will 
be very imperfectly accomplished (the magnetization will be 
far from saturation), and in that case the susceptibility, which 
is the ratio of the magnetization to the strength of the external 
field, will be inversely proportional to the absolute temperature. 


The spectroscopic evidence shows that every c closed ' group 
of electrons in an atom every completed Bohr subgroup, such 
as the two N u electrons, or the two N 2 i together with the four 

N 22 has no resultant magnetic moment. Hence all simple ions 

of the effective atomic number of an inert gas, and the inert gases 
themselves, are diamagnetic. The theory of Langevin enables us 
to calculate from the diamagnetic susceptibilities the average area 
of the electronic orbits, and the results are in approximate agree- 
ment with those required by the sizes of the atoms as deduced 
from the X-ray measurement of crystal structure. While we 
know little about the magnetic moments of the orbits of shared 
electrons, the facts indicate that these also tend to balance one 
another, and we may perhaps assume that as a rule (though not 
always) the two shared orbits forming the covalent link have zero 
magnetic moment. Hence the majority of compounds of the 
lighter elements, and in particular most organic compounds, are 
diamagnetic. Pascal 1 has examined a large number of organic 
substances, and finds that the molecular diamagnetism is made 
up additively of a series of values for the component atoms, 
together with a constitutive term for the type of molecule in 
question : the property thus varies in much the same way as the 
molecular volume. Some approach to an explanation of the 
values of these terms can be made, but the conclusions are 
not yet sufficiently definite to be worth discussing in detail. The 
essential outcome is that while molecules containing para- 
magnetic atoms may or may not be paramagnetic, diamagnetic 
atoms always combine to give diamagnetic molecules, and to 
a first approximation the effects are additive. 2 

1 Ann. Chim. Phys. 1910, 19, 1 : 1912, 25, 289 : 1913, 29, 218. 

2 For further information see Stoner, op. cit., Chapters XII and XV. 

The Bohr Magneton 207 


The investigation of paramagnetic substances has already led 
to important results, and promises to be of the utmost value in 
elucidating the structures both of atoms and of molecules, al- 
though some of the conclusions, especially those dealing with mole- 
cules, must be accepted with reserve until the theoretical and the 
practical sides of the problem have been more fully worked out. 

The first question is whether there is a unit of magnetic 
moment of the atom, as there is a unit of electricity in the electron. 
On purely experimental grounds Weiss claimed to have dis- 
covered such a unit : and this unit, the Weiss magneton, the 
value of which is 18 5 x 10~ 2a ergs/gauss per atom, or 1126 per 
gram-atom, has been commonly adopted. There is a good deal 
of evidence in its favour, but it is by no means "conclusive, and 
can scarcely be expected to be so, in view of the large number 
of magnetons (up to fifty) which have in some cases to be assumed, 
and the difficulty of accurate measurement. It has not been 
found possible to derive the Weiss magneton from the known 
atomic constants. On the other hand Bohr has pointed out that 
there is a very simple relation between the angular momentum 
of an electron (on the quantizing of which his theory is founded) 
and the magnetic moment of its orbit. The angular momentum 
is the product of the mass of the electron, the angular velocity, 
and the square of the radius of the (circular) orbit : 

A = TTi-wr 2 . 

On the classical theory of electromagnetism, if we regard the 
rotating electron (of charge e in electrostatic units) as equivalent 
to an electric current in a circular conductor, the magnetic 
moment is 

_ 1 e-orr 2 
** ~ ~2~^~ ' 
where c is the velocity of light. 

Hence the two quantities have the simple relation 

P- _ 1 e 
A 2 m-c ' 

Now on the Bohr theory (p. 18) the unit of angular momentum 
is h/2Tr (h = Planck's constant). To this therefore there corre- 
sponds a unit of magnetic momentum 

_ 1 e h eh 

^ 2 m-C 2-7T ~ VIC 4:7T ' 

208 Atomic and Molecular Magnetism 

The value of this unit depends only on the mass and charge of 
the electron, and is for a single atom 9 23 x 10" 21 or for a gram- 
atom or gram-molecule 5589 ergs /gauss. This is known as the 
Bohr magneton : it is remarkable that it is almost exactly five 
(4-96) times the Weiss magneton. 

As will be shown in the next section, we have direct evidence 
of the existence of the Bohr magneton. The calculation of the 
moment in Bohr units from the value in Weiss magnetons as 
ordinarily given is complicated by a fact which will be more fully 
discussed later. The Weiss magneton numbers are calculated 
from the susceptibilities on the classical theory, which assumes 
the angles between the magnetic moments of the atoms and the 
field to be distributed at random. It has, however, been shown 
that this is incorrect : only a limited number of values of this 
angle is possible. Hence we cannot obtain b, the value in Bohr 
magnetons, simply by dividing p, that in Weiss magnetons, by 
4-96 : the factor varies somewhat with the magneton number. 
The values are given in the following table, which is due to 
Sommerfeld (Pauli gets values of p about 8 per cent. less). 

b (Bohr) 12345678 10 

p (Weiss) 8 6 14-1 19 3 24-4 29 5 34-5 39 5 44 5 54-5 

The experimental results may be considered under four heads : 
(1) atomic rays (metallic vapours), (2) paramagnetic gases, (3) 
monatomic ions, (4) complex ions. 

1. Magnetic Moments of Atomic Rays 

This subject was investigated with the most remarkable 
results by Stern and Gerlach. 1 The conditions are quite different 
from those in any other magnetic measurements, in that the 
beam of metallic vapour used is at so low a pressure that colli- 
sions between the atoms (with the consequent disturbance of the 
orientation) are excluded. Though the experimental difficulties 
are very great, the principle is simple. A stream of metallic 
vapour issuing from a hole in a minute electric furnace is passed 
through two parallel slits so as to reduce it to a flat parallel beam 
of atoms. This is passed between the poles of a powerful electro- 
magnet so arranged as to give a highly inhomogeneous field, the 
pole-pieces being close together and one of them wedge-shaped. 

1 Stern, Z. /. Phys. 1921, 7, 249 : Gerlach and Stern, Ann. d. Phys. 1924, 
74, 673 : Gerlach, ibid., 1925, 76, 168. See also Gerlach, Materie, Elekln- 
mtdt, Energie, p. 79. Stoner, op. cit., Chapter IX. 

Atomic Rays 209 

The direction of the beam is along the edge of the wedge, and 
its greatest width parallel to the base. The beam is then received 
on a glass plate. The whole apparatus is highly exhausted : the 
temperature is such that the vapour pressure of the metals is 
very low (e. g. 1020 for silver), so that the atoms in the beam 
do not collide with one another, and their velocity can be calcu- 
lated from the temperature by the kinetic theory of gases. The 
number of atoms is so small that their trace is frequently not 
visible on the screen, but it can be made so by a process of 
' physical development ' like that used for under-exposed photo- 
graphic negatives. 

The possible results of such an experiment are these. If the atoms 
have no resultant magnetic moment, the magnetic field will not 
affect them, and the trace will be a narrow line when the field is on, 
as it is when it is off (the diamagnetic effect is too small to be per- 
ceived). If the atom has a moment, it is equivalent to a small 
magnet, and in passing through the field will be deflected towards 
one or other pole according to its orientation, and the more so, 
the smaller the angle between its axis and the field. On the 
classical theory we should expect 'a random distribution of the 
magnetic axes in the beam to start with, and a resulting broaden- 
ing of the narrow line produced in the absence of a field into a 
band thickest in the middle. What is actually observed with 
silver is not this, but that the beam is split into two. This is 
only possible if the atomic magnets, when they reach the intense 
field, are oriented only in two ways half of them (since the two 
beams are as far as can be measured equal in intensity) having 
their magnetic axes parallel, and the other half having them 
antiparallel, to the field. This is entirely opposed to the older 
electromagnetic theory, but is in accordance with the quantum 
theory, which requires that in a magnetic field an atom with 
unit magnetic moment should take up one or other of these two 
positions (space quantization). This result will only be reached 
when, as in these experiments, no collisions between the atoms 
occur : under higher pressures the orientation will be disturbed 
by collisions. The time taken for the orientation in Stern and 
Gerlach's experiments cannot much exceed 10~ 4 seconds ; but 
this time, though short, is long in comparison with the period of 
revolution of the valency electron, which is of the order of KT 16 
seconds. 1 

1 For a further discussion of the problems raised by this phenomenon see 
Einstein and Ehrenfest, Z /. Phys. 1922, 11, 31 : Stoner, op. cit , p. 209. 

3" r >- E e 

210 Atomic and Molecular Magnetism 

The experiment further shows that an isolated neutral silver 
atom has a magnetic moment, and from the separation of the two 
beams we can calculate its amount. The values obtained are 
from 5400 to 5700 ergs /gauss per gram-atom, the value for one 
Bohr magneton being, as we have seen, 5589 ergs /gauss. 
We thus have direct evidence of the validity of the Bohr 

The application of this method to other metals has led to very 
interesting results, although the work has not yet been carried 
very far. Copper and gold, and also sodium and potassium, 1 
have like silver a moment of one magneton, all these elements 
having, in addition to a ' closed ' core, a single electron in an 
N n orbit. Zinc, cadmium, and mercury, all of which have two 
valency electrons in N n orbits, have no magnetic moment, nor 
have tin and lead, which have two N u and two N 2 i orbits. It is 
clear that with the completion of a Stoner grouplet the magnetic 
moment cancels out. Thallium (2 x 6 n and 1 x 6 21 ) is magnetic, 
but the separation is only about one-third of that required for 
one Bohr magneton : this however is to be expected on spectro- 
scopic grounds. Nickel, of which the ' normal ' structure (based 
on the spectrum) is less certain, is peculiar in that the line is split 
up by the field into three, some of the atoms being deflected to 
one side or other to an extent corresponding to two Bohr 
magnetons, and the rest not being affected. Two different 
resolved moments for the nickel atoms are therefore possible. 
Iron, curiously enough, appears to be non-magnetic in the vapour : 
but its low volatility makes the results uncertain. 

A very interesting determination has been made quite recently 2 
of the behaviour of atomic hydrogen, which was found to have, 
like silver and the alkali metals, a moment of one magneton. In 
order to obtain a trace of the beam, it was received on a glass 
screen covered by a thin layer of (white) molybdenum trioxide, 
which was reduced where the hydrogen atoms fell on it to the 
blue dioxide. 

On the whole these experiments, in addition to establishing 
the Bohr magneton and the space quantization, afford a re- 
markable confirmation of the conclusions as to the structures 
of these atoms derived from the spectra and the chemical 

1 Taylor, Phys. Review, 1926, 28, 576. 

a Phipps and Taylor, Phys. Review, 1927, 29, 809. 

Paramagnetic Gases 211 

2. Paramagnetic Gases 

When we leave these highly rarified vapours, and come to deal 
with more concentrated forms of matter, the disturbance of the 
orientation through collisions has to be taken into account. 
This should be most easily done in gases, which are free from 
many complications occurring in the liquid and solid states, and 
it leads directly to Curie's law that (in not too intense fields) the 
susceptibility is inversely proportional to the absolute tempera- 
ture. Oxygen, and the gases with ' odd molecules ' (molecules 
containing an odd number of valency electrons), nitric oxide, 
nitrogen dioxide NO 2 , and chlorine dioxide, are paramagnetic. 
Only two of these have so far been carefully examined oxygen 
and nitric oxide. Oxygen was shown by Curie and by Onnes to 
obey the Curie law from 118 to +450. Its susceptibility and 
that of nitric oxide were examined with great care by Bauer 
and Piccard. 1 Their results afford a strong support for the Bohr 
magneton and the theory of space quantization, the values 
in Weiss units being for oxygen 14-16 (theory for two Bohr 
magnetons 14-1), and for nitric oxide 9 20 (theory for one Bohr 
magneton 86). It might have been expected that nitric oxide 
would be paramagnetic, since it has an ' odd molecule ' : it seems 
natural that as nitric oxide behaves in many ways like an isolated 
univalent radical, it should have the same single Bohr magneton 
as a univalent atom of silver or copper. But it is surprising that 
oxygen should also be paramagnetic. It has a complete core, 
and presumably a complete octet of four unshared and four 
shared electrons, and we should have expected the moments of 
their orbits to balance one another. Hydrogen, nitrogen, the 
halogens, ammonia, sulphur dioxide, carbon dioxide, and organic 
compounds in general (including those which contain oxygen) 
are diamagnetic, and no explanation has been offered of the 
exceptional paramagnetism of elementary oxygen. 

3. Simple Paramagnetic Ions 

Extensive investigations have been made of the paramagnetism 
of ions in solution and in the solid salts, and as far as the mon- 
atomic ions are concerned the relation to the atomic structure is 
at least qualitatively clear. All ions which are composed of 
complete electronic groups both those of inert gas number 

1 J. de Phys. 1920, 1, 97. 

212 Atomic and Molecular Magnetism 

(K + , Ca ++ , F", IT, &c.), and the cations of B metals, with an 
E.A.N. eight units less (Cu + , Zn ++ , Cd**, &c.) are diamagnetic, 
as are the inert gases themselves : from which it follows that all 
simple anions are so. Paramagnetism is only found among those 
ions which contain incomplete electronic groups (transitional 
elements in the wider sense), and the rare earth metals. For 
two of the series of such elements, those of the first long period 
from scandium (21) to copper (29), and the rare earth metals 
from lanthanum (57) to lutecium (71), this conclusion has been 
established in detail. Thus scandium (2) (8) (9) (2) gives an ion 
Sc +++ , which is diamagnetic because it has the complete structure 
(2) (8) (8). The cuprous ion (2) (8) (18) is diamagnetic, while the 
cupric (2) (8) (17), in which the third quantum group is incom- 
plete, is paramagnetic. The ions La" 1 " 1 " 1 " and Ce ++++ , both of 
which have the E.A.N. (2) (8) (18) (18) (8), are diamagnetic, and 
so are Lu +++ and Hf ++++ , with the E.A.N. (2) (8) (18) (32) (8) ; 
but the ions of the intervening elements, in which the fourth 
quantum group contains more than 18 and less than 32 electrons, 
are paramagnetic. 

These conclusions are derived from the study of the suscepti- 
bilities of salts of these ions in solution and in the solid state. On 
the quantitative side there is some uncertainty about them owing 
to the possibility of the values being modified by the formation 
of covalent linkages : this is indicated by the fact that the solu- 
tions and the solids often do not obey Curie's law. 1 Also it must 
be remembered that the theory of the orientation of atoms, and 
of the influence of temperature upon it, was worked out for 
gases, and is less certainly applicable to the ions in a crystal. 
The values in solution are sometimes dependent to a small extent 
on the concentration, and appear to be affected also by hydro- 
lysis and by the formation of auto-complexes. But approximate 
values (at any rate within one Weiss magneton) may be deduced 
for these ions, and the agreement between the values obtained 

1 Many solids obey Weiss's law X = where X is the paramagnetic 


susceptibility, T the temperature, and a constant. C has the same sigmfl- 


cance as in Curie's law X = . Weias's law may be derived by assuming 

that there is mutual interaction between the molecules of the solid, of an 
unknown nature, which is proportional to the intensity of magnetization. 
(If I is the magnetic moment per unit volume, H the magnetic force, and 
d the density, the specific susceptibility per unit mass X = I/H.d.) 

Paramagnetic Ions 


in solution, and those given by the crystalline salts, even the 
oxides \ is surprisingly good. The values to the nearest Weiss 
magneton, and the approximate number of Bohr magnetons, 
are given in the following table, together with, the number of 
electrons in the third quantum group in the ion. 


in 3rd 













K' ? Ca" 






JVLn" Fe'" 





Cu' Zn" 

p (Weiss) 



9 19 20 

24 25 

29 29 





b (Bohr) 



4 4 

5 5 





This shows in the first place that the magnetic moment of the 
ion depends primarily on the number of electrons and not on the 
nuclear charge : it is the same for Cr'", as for Mn"", for Cr" as 
for Mn"', and for Mn" as for Fe'" : this seems to show that it is 
determined rather by the type of orbit than by the firmness with 
which the electron is bound. Secondly there is an evident ten- 
dency for the moment to increase by one Bohr magneton for 
each of the first 5 electrons added to the original 8 in the third 
quantum group, and to fall by 1 for each of the subsequent 5. 
To this however there are certain exceptions : V" is 1 instead 
of 8, Co" is 4 instead of 8, and Ni", which should be 2, gives a value 
between 2 and 8, suggesting an equilibrium between two forms 
of ion. Of the 10 electrons added to the third group as we pass 
from one end of this series to the other, 4 go to the 8 32 grouplet 
and 6 to the 8 33 , but there is nothing in the magneton values to 
indicate that one of these grouplets is completed before the other 
begins to fill : the curve rather suggests that the two processes 
go on simultaneously. 

The magnetic moments of the ions of the rare earth metals 
have been determined independently by Cabrera and Stefan 
Meyer, 2 who used mainly the crystalline hydrated sulphates and 
the oxides. Their values agree well on the whole, considering 
the immense difficulty of purifying the materials. The results 
do not give integral numbers of Bohr units, which may be due 
partly to incomplete purification : it is also possible that the 
assumption that these salts obey Curie's law (which has been 
proved for gadolinium sulphate) is not true for all of them. The 

1 It is assumed that these are polar compounds, or, winch comes to the 
same thing, that the moments of the two shared orbits which constitute a 
covalency neutralize one another. 2 Phys. Z. 1925, 26, 51. 


Atomic and Molecular Magnetism 

values in the following table are the means of those of Cabrera 
and St. Meyer : approximate Bohr magneton values are given 
in the last line. 


in 4th 











La'" Ce"" 

Ce'" Pr"" 







p (Weiss) 


11-4 13-8 






6 (Bohr) 


1-5 1-9 







in 4th 
















Lit'" Hf"" 

p (Weiss) 







A fBohr) 







It is thus evident that the ions with complete fourth quantum 
groups of 18 or 32 electrons are diamagnetic. Between them we 
have the ions in which the grouplets of 6 x 4 43 and 8 x 4 44 are 
being built up. The fact that the curve falls into two parts, the 
first with about five elements and the second with nine, suggests 
that the difference between the energy levels of the grouplets is 
sufficient for the first to be more or less completed before the 
second begins to develop, whereas in the first transition series, 
as we have seen, there is only a single curve, indicating that the 
8 82 and 3 83 grouplets develop together. 1 

Of the two other transition series (Y 89 to Pd 46, and Hf 72 
to Pt 78) only isolated members have been investigated, and 
though the results seem to be of the same kind as in the first 
series, the details are not- yet clear. 

3. Complex Ions 

The salts of these ions have usually been examined in the solid 
state, and as a rule only at one temperature : when the tempera- 
ture has been varied Weiss' s law has often been found not to 

1 The atomic moments of the rare earth metals have been correlated 
satisfactorily with the spectroscopic data by Hund (Z. / Phys. 1925, 33, 

Paramagnetism of Complex Ions 215 

hold. 1 This suggests that the substance is really a mixture of 
two or more forms in equilibrium. It would seem however from 
the regularity of the results that with many salts the error due 
to this cause is not large. 

With well-established complexions having a central atom of 
a transition element, evidence has been adduced by Welo and 
Baudisch 2 that the paramagnetism depends primarily on the 
effective atomic number : that when this has the same value as 
in an inert gas, the complex is diamagnetic, while if it differs 
from this by n units, the complex has a magnetic moment of 
n Bohr magnetons. Thus the six-covalent ferricyanides, as 
K 3 [Fe(CN) fl ] 5 with an E.A.N. 26 + 6 + 3 = 35, give p = 10 (b = 
ca. 1), while the ferrocyanides, as K 4 [Fe(CN) 6 ] (E.A.N. 26 + 
6 + 4 = 36, the atomic number of krypton) are diamagnetic. 
Replacement of CN groups by NO 2 NH 3 , H 2 O, &c. (with the 
change of electrovalency required to preserve the E.A.N.), has 
no effect. So too the cobaltammines of the well-known series 
with E.A.N. 36 (from K 3 [CoX 6 ] to [Co(NH 3 ) 6 ]Cl 3 ) are aU dia- 
magnetic, while the chromammines, with the exactly corre- 
sponding formulae, and accordingly an E.A.N. of 33, all give 
approximately p = 19, or b = 3. The results are summarized 
by Stoner in the following table : 


37 38 



Thus the nearest Bohr magneton value is in all cases equal to the 
difference between the E.A.N. of the central atom and 36, the 
atomic number of krypton. The rule does not appear to hold 
any longer after the third quantum group of 18 has become 
firmly established, for the ethylene-diamine compound of zinc 
chloride [Zn(en) 3 ]Cl a (E.A.N. 40) is diamagnetic. It should be 
noticed that the bichromates and permanganates, in which the 
central atom has the E.A.N. 26 = (2) (8) (8) (4, 4), consisting 
entirely of completed groups and a fully shared octet, are dia- 
magnetic, or at most very weakly paramagnetic. 

A few measurements have been made with complex ions of 
metals of the palladium and platinum series, which show that 

1 Rosenbohm, Z. phys. Chem. 1919, 93, 693. 

2 Welo, Nature, 1925, 116, 359 : Jackson, ibid., 360 : Welo and Bau- 
disch, ibid., 606. 








At. No. . . 







E.A.N. . . . 







p (Weiss) 





b (Bohr) approx. 





216 Atomic and Molecular Magnetism 

the salts are diamagnetic when the E.A.N. of the central atom 
is that of xenon or emanation. Thus [Rh(en) 8 ] C1 3 , E.A.N. 54, is 
diamagnetic, and so are [Ir(NH 3 ) 6 N0 2 ]Cl 2 and [Pt(NH 8 ) 4 Cl 2 ]Cl 2 , 
both of which have the E.A.N. 86. But the four-covalent com- 
pounds of platinum and iridium such as K 2 [PtCl 4 ], in all of which 
the E.A.N. is 84, are diamagnetic likewise. 

These results are of unusual interest, and if they can be 
extended and confirmed will give us a new and powerful means 
of investigating the constitution of complex molecules. Some 
examples of this may be given. The constitution of the metallic 
carbonyls is a very difficult problem. The existence of carbon 
monoxide is itself surprising, but we have had to recognize that 
carbon with an E.A.N. of (2) (2, 2, 2) is comparatively stable. It 
remains to devise a stable attachment of this to a central atom. 
Though the formulae of the mixed carbonyl compounds tend to 
show that a CO can replace an NH 3 , and so must be attached by 
a single covalent link, the evidence is not conclusive. If however 
we can trust the magnetic argument, the question is answered 
at once. Ni(CO) 4 and Fe(CO) 5 are both diamagnetic, and so the 
central atom in both should have an E.A.N. of 86 : for nickel 
28 + 8, and for iron 26 + 10. If so, each carbonyl group must 
contribute two electrons to the central atom, and the structure 
is presumably Ni--C=0 and Fe-<-C=O. If this is true, the 
stability of the compounds is very remarkable : we know no 
other stable compounds of trivalent carbon with the E.A.N. 
(2) (3, 3). Another puzzle is the structure of the ' nitroxyl ' 
compounds, which contain the NO group in a complex. Now 
it is found that Na 2 [Fe(CN) 5 NO] and [Ru(NH 3 ) 4 Cl(NO)]Br 2 are 
diamagnetic. We should infer that the effective atomic numbers 
of the metals in these complexes are 86 and 54 respectively. 
This involves the contribution of three electrons by the NO to 
the central atom : 

Fe26+5+3+2 = 36: Ru 44 +8 +1+3 -2 = 54. 

This rule relating the magnetism to the E.A.N. raises a question 
as to the state of the simple ions of the transition elements in 
solution. As we saw in the last chapter, the natural assumption 
is that these simple ions, as they are of small size and have a 
valency greater than 1, are in water practically wholly in the 
hexahydrated form, as [Fe(H 2 O) fl ] ++ , &c. ; the readiness with 
which many of them form stable six-covalent compounds with 
ammonia supports this view. In that case their real E.A.Ns. in 

Transitional Elements 217 

solution are twelve units higher than those calculated for the 
simple ions : the ferrous ion, for example, will have an E.A.N. 
not of 24 (26 2), but of 36 (26 2 +12). Hence on the principles 
which appear to hold for the complex ions discussed above, it 
should be diamagnetic, whereas it actually has a moment of 
four Bohr magnetons. The agreement between the values obtained 
in solution and those given by the crystalline salts (many of 
which are anhydrous, and which include the chlorides) is also 
difficult to explain, as it is hard to see how in the solids, even if 
they are not ionized but covalent, the metallic atom can form as 
many as six-covalent links. It is, however, worth pointing out 
that if we assume that in solution these ions form not the hexa- 
hydrates but the tetrahydrates, a considerable number of them 
obey approximately the rule of Welo and Baudisch. The follow- 
ing table gives (1) the ionic symbol, (2) the E.A.N. of the tetra- 
hydrated ion, (3) the difference between this and the atomic 
number of krypton, and (4) the observed number of Bohr 

Ion Cr'" Mn"" Mn'" Cr" Mn" Fe'" Fe" Co" Ni" Cu" 
E.A.N. (4H 2 O) 29 29 30 30 31 31 32 38 84 85 
30 E.A.N. 77 66554321 

6 obs. 8 8 4 4 5 5 ca. 442-31 

The results agree with the rule fairly closely (with the exception 
of cobalt) for the ions from Mn" to Cu" : in fact on this hypothesis 
the moment should fall from 5 for Mn" and Fe"' by steps of 
1 to 1 for Cu", which as we have seen is what the whole curve for 
the simple ions leads us to expect. The earlier members of the 
series do not fall into line : the magneton values fall as we go 
backwards from Mn" instead of continuing to rise ; but of course 
we have no evidence from the behaviour of the complex ions as 
to whether Welo's rule holds when the difference between the 
E.A.N. and the inert gas number is greater than three. The 
coincidence among the later members of the series may be merely 
accidental, but it is worth noticing, especially as a covalency of 
four is quite possible in the solid salts, though it is difficult to 
see how one of six could arise. Such a structure as 

CK Cl 

v / 


/ s cr ci 

is not improbable in view of the great stability of 4-covalent 
compounds in general. An X-ray examination of these crystals 
would be of interest. 

3062 P f 


Atomic and Molecular Magnetism 

It will be seen that the magnetic properties of atoms and mole- 
cules show promise of becoming of the utmost importance. The 
theory, although it has made great progress in the last few years, 
is by no means complete, and many of its conclusions cannot 
yet be regarded as definitely established. It is only recently 
that the magnetism of electronic orbits has been seriously 
attacked from the physical side, and the extension of the theory 
to shared orbits has not yet even begun. The experimental work 
also offers peculiar difficulties, and the data are still compara- 
tively scanty. But the magnetic properties afford a new and 
independent means of attack on the problem of molecular 
structure, and one which has the advantage of being applicable 
to non-volatile substances in the dissolved and solid states, 
whereas the spectroscopic method breaks down under such con- 
ditions owing to the broadening of the lines. There is scarcely 
any branch of the inquiry which seems more likely than the 
magnetic to lead to important developments during the next 
few years. 


WE have next to consider the evidence bearing on the 
arrangement in space of the groups covalently linked to 
an atom, and the relation of this to the nature of the atom and the 
number of the attached groups. 

The simplest assumptions are that four groups will be arranged 
at the points of a tetrahedron, six at those of an octahedron, and 
eigfflPat those of a cube. These may be called the tetrahedral, 
octahedral, and cubic arrangements respectively, and correspond 
to the orientation on the Bohr theory of the grouplets of four, 
six, and eight electrons : they are also of course supported to 
a very considerable extent by the stereochemical evidence. At 
the same tune a plane distribution is not impossible, and there 
is evidence of its occurrence with certain 4-covalent atoms. 

With carbon van't Hoff and Le Bel independently suggested 
in 1874 that the four attached groups do not lie in a plane, and 
van't Hoff proposed the tetrahedral arrangement which has 
never since been disputed. The deduction from this theory, that 
the four groups attached to two doubly linked carbon atoms in 
a compound of the type abC=Cab must lie in a plane, was made 
at the same time by van't Hoff, and has held its ground likewise. 
All the later developments of the stereochemistry of carbon are 
nothing more in principle than experimental proofs of deductions 
from van 't Hoff's original idea. 

Compounds showing optical activity due to the arrangement 
of groups round a nitrogen atom l were first 2 obtained in 1899 
by Pope and Peachey 3 when they resolved a salt of benzyl- 
phenyl-allyl-methyl-ammonium. In 1908 Meisenheimer 4 showed 
that methyl-ethyl-aniline oxide could be separated into its active 

1 The possibility of a tetrahedral distribution in an ammonium ion was 
suggested in 1878 by van 't Hoff (Ansichten liber die org. Chemie, p. 80). 

a Le Bel in 1891 (C. R. 112, 724) claimed to have obtained a solution of 
a methyl-ethyl-propyl-isobutyl-ammonium salt of small rotation by allow- 
ing a mould to grow in it. Marckwald (Ber. 1899, 32, 560) could not repeat 
this, but Le Bel (C. R. 1899, 129, 548) published a confirmation of his earlier 

3 J. C S. 75, 1127. * Ber. 1908, 41, 3966. 

220 Stereochemical Relations 

components by means of its d-bromocamphor-sulphonate, and 
that the liberated base, 

CH, CH 3 . yOH 

r H -_N:=O , or more probably in solution C 2 H 5 -;Nv 

*-2 jrA c/ x ^ ' -p rr / \rktr 

C 6 H 6 / C O H B H 

(as these compounds were then formulated), retained its optical 
activity. Whichever be the correct formula, this proves that 
a nitrogen atom attached to only four different groups (not five) 
can be optically active, whereas if it has two similar alkyl groups 
we know that the activity disappears. Meisenheimer concluded 
that four of the groups attached to an ammonium nitrogen atom 
are arranged tetrahedrally, and that the fifth (ionized) group 
occupies no fixed position. This is of course in complete agree- 
ment with our modern views of the nature of polar and non-polar 
linkages. Although Meisenheimer's evidence is strong, and the 
development of the theory of electrovalency has further strength- 
ened it, it is not absolutely conclusive : the possibility of the 
five groups attached to a nitrogen atom occupying the points of 
a square pyramid (as suggested by Bischoff in 1890, and accepted 
by H. O. Jones in 1905) is not definitely excluded. The final 
proof of the tetrahedral structure was given by Mills and Warren. 1 
They prepared 4-phenyl-4'-carbethoxy-bispipcridinium-l : 1'- 
spiran bromide 

Hx^ /CHa-CEU /CH Z -CH 2 \ /H 
C 6 H B X ' ^CHa-CH/ ^CHa-CH^ ^CO-jEt 


and resolved it through the bromocamphor-sulphonatc : this 
gave an optically active bromide ([M]507). The original 
compound is formed with a readiness which indicates that there 
can be little strain in the two rings. It can easily be seen on a 
model that if the two rings are attached to the base of a square 
pyramid, the molecule will have a plane of symmetry, whereas 
if they are attached to the points of a tetrahedron it will not. 
Thus the pyramidal structure is shown to be incorrect, and 
the tetrahedral is confirmed. This is precisely what we should 
expect on the electronic theory, since the neutral carbon atom 
and the positively charged nitrogen have the same number of 

The distribution of the groups in compounds of trivalcnt nitro- 

1 J. C. S. 1925, 127, 2507. 

Nitrogen 221 

gen of the type Nabc is still a matter of some doubt. The electro- 
nic theory does not at present help us to answer this question. 
If the three groups attached to the nitrogen have the same 
relative positions as three of the four in an ammonium ion, the 
molecule will obviously be asymmetric ; but even then it is not 
improbable that the antimers may change into one another so 
easily in the absence of a fourth group that the compound will 
be permanently racemic. It is also conceivable that when the 
fourth position is unoccupied the orbits may be so far distorted 
that the three lie in the same plane with the nitrogen atom. On 
the theoretical side therefore the question is open. 1 All attempts 
to prepare optically active compounds of the type Nofo have 
failed. Meisenheimer has recently a reviewed the subject, and 
come to the conclusion that singly linked trivalent nitrogen 
(except possibly when it forms part of a polycyclic system, as in 

g CH 2 

cannot give rise to optical activity. He considers that the groups 
do not lie in a plane, but that the molecule changes continuously 
from one asymmetric form to the other, and that this process 
is only arrested when the fourth covalency is occupied. 

Where two of the covalencies of trivalent nitrogen are 
attached to the same atom, it can be shown that the third is not 
in the same plane with the other two. This conclusion was made 
very probable by the explanation which it gave of the isomerism 
of the oximes, 4 and later of the diazo-compounds (Hantzsch) ; 
it was definitely proved by the work of Mills and Bain 5 for the 
oximes, and subsequently by the same authors 6 for the hydra- 
zones and semicarbazones. 

The tetrahedral symmetry is therefore established for carbon 
and 4-covalent nitrogen. Of the other elements in the first 
short period, it has been proved to occur with beryllium and 
boron, and almost certainly with oxygen. With beryllium its 
occurrence was made probable by the work of Lowry and 
Burgess, 7 who showed that beryllium benzoyl camphor (in which 

1 For a further discussion of this point see below under sulphur (p. 228). 
a Meisenheimer, Angermann, Finn and Vieweg, Ber. 1924, 57, 1744. 

3 See Ann. 1920, 420, 190 

4 Hantzsch and Werner, Ber. 1890, 23, 11. 
6 J. C. S. 1910, 97, 1866. 

8 Ibid., 1914, 105, 64. 7 J. C. S. 1924, 125, 2081. 


Stereochemical Relations 

the metallic atom forms part of two unsymmetrical rings) under- 
goes considerable mutarotation in solution. As in this compound 
the mobile hydrogen atom of the benzoyl camphor is replaced, 
it is difficult to see how the mutarotation can be due to anything 
but a racemization of the groups attached to the beryllium 
atom : in which case the arrangement round this atom must 
be tetrahedral. A more definite proof was provided by Mills 
and Gotts, 1 who resolved the beryllium compound of benzoyl- 
pyruvic acid 



The alcoholic solution of the brucine salt, when quite pure, 
showed a mutarotation from [a] 39-9 to [a] 18-1 in three hours. 
By adding the brucine salt to a solution of dimethylamine hydro- 
chloride in alcohol, nearly the whole of the alkaloid was precipi- 
tated as the hydrochloride, and the nitrate, measured at once, 
had a rotation a = +1-13, which sank in fifteen minutes to 0-1. 

With boron the same conclusion was established by Boeseken 
and Meulenhoff, 2 who prepared the strychnine salt of borosali- 
cylic acid, 



and by recrystallization from water obtained a dextrorotatory 
fraction ([a] +22-6). As strychnine and its salicylate are both 
laevorotatory, this showed that the boron complex was dextrorota- 
tory. Both the free acid and its salts racemized very rapidly, and 
they could not be obtained in the active form. That the same 
distribution occurs with 4-covalent oxygen is indicated by 
the work of Morgan and Bragg 3 on the basic acetate of beryllium 
Be 4 0(0 CO-CH 3 ) fl . They showed that the molecule of this com- 
pound (which is not ionized) is a regular tetrahedron, with 
an oxygen atom at the centre, and four beryllium atoms 

1 J. C. S., 1926, 8121. 

a Proc. K. Akad. Wetensch. 1924, 27, 174 : J. C. S. Abstr. 1924, i. 776. 

3 Proc. Roy. Soc. 1923, 104, 487. 

Werner's Metallic Compounds 223 

at the corners. The same structure 1 must also occur in the 
analogous zinc and zirconyl compounds Zn 4 0(0-C0 CH 3 ) 6 and 
(ZrO) 4 O(0-CO-CH 3 ) 6 . It might be argued that this only shows 
that the four valencies of the oxygen atom can assume this 
arrangement under strain ; but the remarkable stability of the 
compound, and the great readiness with which it is formed, 
indicate that there is no considerable strain in the molecule. 

Thus we have good evidence that the atoms of five of the 
seven valent elements of the first short period have, in the 
4-covalent state, the four groups arranged tetrahedrally round 
them ; and we may take it that this is the only arrangement 
possible for elements whose maximum covalency is four. 

With the heavier elements, whose maximum covalency is 
six or eight, we have definite proof that in the 6-covalent form 
(nothing is known at present about the spatial distribution of 
eight covalencies) many of them have the six groups placed at 
the points of an octahedron. This has been proved by the test 
of optical activity for chromium, cobalt, iron, rhodium, iridium, 
arsenic, and aluminium. 

In 1911 Werner was able to resolve the 6-co-ordinated 
cobalt compounds with two and three chelate groups, such as 
[CoCl(NH 3 )(en) 2 ]X 2 2 , [CoClN0 2 (en) 2 ]X 3 and [Co(en) 3 ]X 3 4 into 
their optical antimers, and thus established his octahedral theory 
for this element ; the final proof that the activity was not due 
to some conceivable rearrangement of the organic groups was 
given when he resolved 6 the complex compound 


which contains no carbon at all. He further prepared opti- 
cally active compounds containing ' asymmetric atoms ' of 
chromium, 6 iron, 7 and rhodium. 8 The resolution of an asym- 
metric compound of iridium, K 3 [Ir(C 2 4 ) 3 ], was effected by 
Dele'pine. 9 Recently Rosenheim and Plato 10 have obtained an 

1 The structure will be discussed in Vol. II under Berylbum. 

* Ber 1911, 44, 1887 (en = ethylene diamine). 
3 Ibid., 2445, 3272, 8279. 

* Ber. 1912, 45, 121. Ber. 1914, 47, 8087. 

8 [Cr(en) 2 Cl 2 ] X, Ber. 1911, 44, 8132 : K 3 [Cr(C 2 O 4 ) 3 1, ibid., 45, 3061. 
7 Ibid., 1912, 45, 483. " jbi&., 45, 1228. 

9 Bull. Soc. Chim. 1917 [4], 21, 157. 
10 Ber. 1925, 58, 2000. 

224 titereochemicaL Relations 

optically active compound of 6-covalent arsenic. The cin- 
chonine salt of tricatechol-arsenic acid 


on crystallization from alcohol separated entirely as the salt of 
the Z-acid (owing presumably to continuous racemization in 
solution). From this the free acid and its potassium and barium 
salts were obtained, which showed high activity. The conditions 
of racemization of these compounds are obscure ; the salts 
appear to be unaffected by hot water or alkaline solutions, but 
are at once racemized by traces of acid. This work is of peculiar 
interest because, as we shall see, arsenic has been shown to have 
a tetrahedral structure in its 4-covalent compounds : it is 
so far the only element which has been proved to give optically 
active compounds both of the tetrahedral and of the octahedral 
type. Aluminium has been found 1 to give an optically active 
6-covalent compound in its trioxalato-salt 

M 3 

The strychnine salt on extraction with cold water leaves behind 
a less soluble fraction from which ammonium iodide precipitates 
the strychnine as iodide, while the ammonium salt 

(NH 4 ),[Al(C a 4 )J 

remains in solution. This gives a rotation [M] D +81 2, which 
falls to half its value at the ordinary temperature in forty-five 

We may thus take it as proved that the octahedral arrange- 
ment is that of the 6-covalent compounds of many elements, and 
may assume with some probability that it is that of 6-covalent 
compounds in general. 

Among the 4-covalent compounds of elements heavier than 
fluorine (i. e. with a maximum covalency of six or more) we find 
a more complicated situation. Two different spatial arrange- 
ments occur : the tetrahedral, giving optical activity under the 
same conditions as with carbon or nitrogen, and a plane arrange- 
ment, which cannot give optical activity at all, but leads to the 

1 Wah.1, Ber. 1927, 60, 399. 

r /,o-c=o\ ~| 

AlK I 1 . 

L \^o-c=oj I 

Silicon : Phosphorus 225 

production of two chemically isomeric forms of any compound 
of the type X0 2 & 2 which is of course impossible with a tetrahedral 
disposition of the groups. 

Tetrahedral symmetry optical activity with four different 
groups has been established for silicon, phosphorus, sulphur, 
selenium, arsenic, copper, zinc, and probably tin. The silicon 
compounds x were (1) the substituted silicoethers 

SO 3 H-C a H 4 'CH 2 -Si Si-CH 2 -C 6 H 4 -SO 3 H 

C 4 H 9 C 
and (2) substituted silicanes 

C 6 H B -CH 2 -Si-CH 2 -C 6 H 4 .S0 3 H . 
C 3 H 7 

Though the success of the resolution can scarcely be doubted, 
the rotation was exceedingly feeble. With phosphorus Meisen- 
heimer 2 has shown that the spatial relations of the amine oxides 
are repeated in the phosphine oxides : methyl-ethyl-phenyl- 

phosphine oxide C a H 6 ^P->O was resolved through the 


bromocamphor-sulphonate, and was found to have a molecular 
rotation of about 40 in water. This is the only type of phos- 
phorus compound in which optical activity has been definitely 
proved. Kipping 3 has obtained indications that the unsym- 
metrical djaryl hydrogen phosphates, such as 

0-P(OC 10 rf 7 

exist in active forms, but this cannot be said to have been 

With arsenic numerous unsuccessful attempts have been made 
to resolve both the arsonium salts and the arsine oxides. Burrows 
and Turner 4 claimed that they had obtained active d-phenyl- 
naphthyl-benzyl-arsonium iodide, but the maximum rotation 
they obtained was only 0-1 in a 2-dm. tube. Mills and Raper 5 

1 Kipping, J. C. S. 1907, 91, 200, 717 : 1908, 93, 457. 

2 Meisenheuner and Lichtenstadt, Ber. 1911, 44, 356. 

3 Kipping and Challenger, J. C. S. 1911, 99, 626. 

* J. C. S. 1921, 119, 426. B J. C. S. 1925, 127, 2479. 

306* G 

226 Stereochemical Relations 

finally obtained definite proof by the resolution of _p-carboxy- 
phenyl-methyl-ethyl-arsine sulphide 

yC 6 H 4 -COOH 

This substance was chosen because the sulphide has none of the 
basic properties of the oxide, and the arsenic atom is thus pro- 
tected from disturbance in the course of the separation, the 
necessary salt formation being performed by the remote carboxyl 
group. The acid was resolved through the brucine and morphine 
salts, and had a rotation of about [M] 55. It showed no tendency 
to racemize. 

The resolution of optically active 4-covalent cupric and zinc 
compounds was effected by Mills and Gotts, 1 as with beryllium, 
by means of the benzoyl-pyruvic acid derivative. The alkaloidal 
salts in both cases showed very rapid mutarotation (the half -life 
period was about five minutes), but the activity was sufficiently 

Thus the 4-covalent compounds of silicon, phosphorus, 
arsenic, copper, and zinc show essentially the same relations as 
those of carbon and nitrogen, although the smaller stability of 
the substances makes their investigation less easy. 

The only other elements after the first short period which have 
been shown to act as centres of asymmetry in molecules in which 
they have a covalency of less than six, are sulphur, selenium, and 
tin. The behaviour of these elements raises a question of great 

In 1900 Pope and Peachey 2 prepared the bromocamphor- 
sulphonate of methyl-ethyl-propyl tin, 

CH 3 v X 
/ Sn \ 

C 3 H 7 

C 2 H 6 X 

The salt that crystallized from water was the d-base-d-acid com- 
pound, which indicated in a freshly prepared solution a cationic 
activity of about [M] +45 ; but the mother liquor on evapora- 
tion gave a further crop of the same salt (and no Z-base-d-acidsalt) 
owing presumably to continuous racemization during evapora- 
tion. 3 The iodide obtained from this salt had a rotation of [a] 
+23 as a maximum, but racemized very easily. The experi- 

1 J. C. S. 1926, 3121. 2 Proc. C. S. 16, 42, 116. 

8 Compare the similar behaviour of the 6-covalent arsenic compound, 
p. 224. 

Arsenic : Tin : Sulphur 227 

ments were not continued, mainly on account of the physio- 
V logical properties of the substances, but the results seem beyond 

doubt ; for it was shown that the bromocamphor salt when first 
dissolved in water had an activity of +818 and gave with 
potassium iodide an active iodide : that after the solution had 
been heated on the water bath for two hours its activity fell to 
+275, and the iodide which it now formed was inactive : and 
finally that from this heated solution there crystallized out on 
evaporation the original dextro-dextro salt. The same authors 
in the same year 1 resolved the camphor-sulphonate and the 
bromocamphor-sulphonate of methyl-ethyl-thetine 

C 2 H B X 

by recrystallization from alcohol and from acetone, and precipi- 
tated the sulphur base as its platinichloride B 2 [PtCl 6 ], which they 
showed to have an activity in water of about 80. At the same 
time Smiles 2 resolved the -fcketiete * f\n\d- IA :<' '7 

CH 2 -CO.C 6 H 6 

C a H 5 X 

in the same way. This was repeated and confirmed by Pope 
and Neville, 3 who showed that the picrate of Smiles's base had an 
activity of about 85 ; the activity persisted in the platini- 
chloride. In the same paper Pope and Neville describe the 
resolution of the analogous selenitine 

CH 3 \ /CHa-COOH 

by the same methods. The platinichloride has a molecular rota- 
tion of 55. For some unknown reason both the sulphur and 
the selenium compounds, while they retain their activity in the 
form of camphor- and bromocamphor-sulphonates, picrates, and 
chloroplatinates, lose it at once if they are converted into the 
double mercuric halides B[HgCl 3 ] and B[HgI 3 ]. 

These results are very remarkable, because in every case the 
active compounds have one of their four groups attached by an 
ionized link. They are all of the type [MR 1 R 2 R 3 ]X S where 
Rj R 2 R 3 are organic radicals, and X is the anion of a strong acid 
such as hydriodic, bromocamphor-sulphonic, or chloroplatmic. 

1 J. C. S. 1000, 77, 1072. a Ibid., 1174. 

3 Ibid , 1902, 81, 1557. 

228 titereochemical Relations 

There is no doubt that they can be ionized without the activity 
disappearing. This would seem to show that the groups occupy- 
ing three points of a tetrahedron can retain their positions even 
when the fourth point is unoccupied. It was suggested by 
Meisenheimer 1 that these complex ions never exist as such : 
that in the absence of water the molecules are covalent, and that 
their ionization by water is due to the direct replacement of the 
anion by a co-ordinated water molecule 

a c ra, 


so that the central atom is never really trivalent. 2 

The existence of asymmetric molecules with only three groups 
attached to the central atom has been definitely proved in the 
last two years by the work of Kenyon and Phillips, who have 
resolved sulphinic esters, 3 unsymmetrical sulphoxides, 4 and the 
sulphilimines G of Mann and Pope 


all of which must owe their activity to the arrangement of the 
three groups round the sulphur atom. This work is of interest 
in the first place as giving independent evidence of the existence 
of these co-ordinate links. It is clear that on the older formulae, 
in which the sulphoxide, for example, is written with a doubly 


linked oxygen -p ^>S = 0, asymmetry is impossible, since two of 


the valencies of the sulphur are attached to one single atom : the 
three groups must lie in the same plane with the sulphur. The 
only possible formula for an asymmetric molecule is one in 
which the sulphur is joined to the oxygen by a single link, and 
since the stability of the compound shows that the octet of the 
oxygen must be complete, this link must be formed of two 
electrons derived from the sulphur. This conclusion is also sup- 
ported by Sugden's measurement of the parachor of the sulphi- 
nate in question. 

We are thus compelled to admit that in these compounds 

1 Ber. 1924, 57, B. 1744. * See farther, p. 229, note. 

8 Phillips, J. C. S. 1925, 127, 2552. 

4 Hamson, Kenyon, and Phillips, ibid , 1926, 2079. 

5 Clarke, Kenyon, and Phillips, ibid., 1927, 188. 

Tri-covalent Sulphur 229 

the three groups can retain their places in spite of the fact that 
V the fourth point of the tetrahedron is unoccupied. The same is 
presumably true of selenium, and probably of tin, in the com- 
pounds described above. There is no objection to be raised to 
this on physical grounds ; the only difficulty is to explain why 
the trivalent nitrogen atom, which has precisely the same electro- 
nic arrangement, should have been found to be incapable of 
giving active forms. Phillips points out that in every instance 
where a tri-covalent atom has been found to act as a centre of 
asymmetry, that atom is positively charged, either as a cation 
(in [RjRaRgMJX, where M = S, Se, or Sn) or as a donor (in 
RjRaS-^O and RjRgS-^-NR) ; and he suggests that it is the 
presence of this charge which prevents the racemization of the 
molecule. This conclusion can scarcely be accepted without 
further evidence. The proof that activity is impossible in the 
* absence of such a charge rests on the single case of nitrogen : no 
other trivalent element has been investigated in sufficient detail. 
The physical arguments are not definite enough to be of value in 
the present state of our knowledge, and the question can only be 
settled by further experimental work. 1 

So far it appears that elements with a maximum covalency 
higher than four, when they form tri- or quadri-covalent com- 
pounds, have the groups arranged tetrahedrally. But this is not 
always so. Some elements form compounds in which the four 
groups certainly lie in a plane. The first examples of this were 

recognized by Werner 2 in the 4-co-ordinated platinous com- 

1 Meisenheimer's suggestion, that the central atoms in the salts [R 3 S]X, 
[R 3 Se]X, and [R 3 Sn]X are really 4-covalent, replacing a covalent X* 
group by a co-ordinated H 2 O when they ionize in water, is thus seen to be 

^ unnecessary to explain the activity of the sulphur and presumably of the 

selenium compounds. It is not supported by the properties of the sul- 
phonium compounds, which are those of true salts , they are non- volatile, 
and like ammonium salts are precipitated from alcoholic solution by ether 
in a non-sol vated form. It is not so certain that Meisenheimer's view is 
wrong in the case of tin. The alkyl-tin salts, like stannic chloride itself, 
may well assume a covalent form in the absence of ionizing solvents, and 
only become ionized by solvation. This distinction between the two classes 
of compounds is supported by the difference in the structure of the central 
atoms. Whereas the sulphur and selenium ions, as formulated without 
hydration, contain complete octets (2, 3, 8), as does a trivalent nitrogen 
atom, the tin compound can only complete its octet either by recombina- 
tion with its anion, or by co-ordination with a molecule of solvent : 
[R 3 Sn]+: 8, 8. [R 3 SnX], [R 3 Sn(OH 2 )] + : 4, 4. 

2 Z. anorg. Chem. 1893, 8, 310. 

230 Stereochemicai iteianons 

pounds of the type [Pt(NH 3 ) 2 Cl 2 ] : these all occur in two chemi 
cally and physically different forms, which is only possible if th 
four groups lie in the same plane with the central atom, admittin, 

Cl Cl 

of a cis Cl-Pt-NH 3 and a trans NH 3 -Pt-NH 3 

NH 3 Cl 

arrangement. This isomerism is widely distributed among th 
4-covalent platmous derivatives ; it is found not only in a variety c 
un-ionized compounds of the diammme series, but also incomple 
ions both positive and negative : it occurs in the pyridme deriva 
tives of the tetrammine series [Pt(NH 3 ) 2 py 2 ]Cl 2j 1 and also in th 
salts K 2 [PtCl 2 (NH 2 S0 3 ) 2 ]. 2 Werner's interpretation was recentl 
challenged by Reihlen, 3 but it has been vindicated by Hantzsch. 
The isomeric compounds of the diammine type are usually ver 
insoluble, and their molecular weights were not determined b 
Werner. Reihlen found that the chlorides [Pt(NH 3 ) 2 Cl 2 ] wer 
soluble in liquid ammonia, and that m this solvent, while 1 Werner' 
cis compound had the normal molecular weight, his trans com 
pound was bimolecular. Reihlen concluded that the isomerisr 
was solely due to the polymerization, and that no inferenc 
could be drawn as to the spatial distribution of the four groups 
Hantzsch found that the corresponding pyridine compound 
[PtClapysj] (which exhibit the same isomerism) are soluble i 
phenol, and showed that they both give normal molecular weight 
by the" cryoscopic method in this solvent. Werner's view tha 
the isomerism is due to the arrangement of the four groups rouni 
the platinum, and that these must therefore lie m the same plan 
with the metal, is thus fully confirmed. 

Similar relations are stated to hold with cobalt, 5 but the evi 
dence i& inconclusive. The cobaltous halides on treatment in th 
dry state with ammonia yield diammines Co(hal) 2 , 2NH 3 , am 
these can be obtained in two differently coloured forms ; fo 
example the chloride in the a-form is pink and in the -form blue 
The blue form on heating goes over into the pink. No othe 
definite differences could be established, as neither form wi 
dissolve in any solvent without decomposition. Until furthe 

1 Jorgensen, Chem. 1886 [2] 33, 510. 

2 Kirmreuther, Ber. 1911, 44, 3115. 

3 Reihlen and Nestle, Ann. 1926, 447, 211. 

4 Ber. 1926, 59, 2761. 

8 Biltz and Fetkenheuer, Z. anorg. Chem. 1914, 89, 97. 

Four Valencies in a Plane 231 

evidence is forthcoming, no conclusions can be drawn from these 
facts as to the nature of the isomerism. 1 

The only element other than platinum which has been proved 
to give 4-covalent compounds in which all the groups lie in 
a plane is tellurium. Vernon a has shown that the product 
Te(CH 8 ) 2 l2 obtained from tellurium and methyl iodide occurs in 
two forms. The original (a) iodide yields in solution a hydroxide, 
from which it can be re-formed. But if this hydroxide is heated 
it is converted (presumably through the oxide (CH 3 ) 2 Te =O) into 
an isomer, which differs in chemical and physical properties from 
the original hydroxide, and on treatment with hydriodic acid 
forms a different () iodide. The isomeric bromides and chlorides 
were also prepared. The molecular weights of both forms of all 
three halides were determined (by the boiling-point in acetone, 
and by the freezing-point in benzene and nitrobenzene), and were 
found to be normal. It is remarkable that the two forms differ 
greatly in their physiological effects, the a being far more power- 
ful than the ft. This isomerism must be due, like that of the 
platinous compounds, to the four groups lying in a plane, and the 
method of transformation indicates that the first product is a 
trans compound, whose hydroxide can lose water only by going 
over to the cis (as fumaric acid forms maleic anhydride), from 
which the second ()8 = cis) iodide is produced : 


CH 3 -Te-CH 3 


a : trans a : trans 


I * 

CH 3 -Te-OH -+ CH,-Te-I 


H I 

: cis j8 : cis. 

The evidence therefore indicates that a four-covalent atom, if 
it belongs to the first short period, and is thus exerting its maxi- 

1 The numerous alternative formulae possible for such compounds when 
their molecular weights are unknown are illustrated by the platinum com- 
pound [Pt(NH 3 ) 2 Cl2], of which, in addition to the two monomeric isomers 
described above, there exist two dimeric forms [Pt(NH 3 ) 4 ] [PtClJ and 
[Pt(NH 3 ) 3 Cl] [Pt(NH 3 )Cl 3 l, and two trimenc forms [Pt(NH 3 ) 3 Cl] 2 [PtClJ 
and [Pt(NH 3 ) 4 ] [Pt(NH 3 )Cl 3 ] 2 , the structures of all of which are quite well 
established. a J. C. S. 1920, 117, 86, 889 : 1921, 119, 105, 687. 

232 Stereochemical Relations 

mum covalency, always has the four attached groups arrange' 
tetrahedrally. If it is an element of a higher atomic number, an 
accordingly has a maximum covalency of six or more, it may sti 
have this arrangement, and is found to do so in most of th 
instances which have been examined (Si, P, S, Cu, Zn, As, Se, Sn' 
But a plane arrangement is also possible, and has been establishes 
for the two elements tellurium and platinum. It is unfortunat 
that the number of elements for which this property has bee 
determined is too small for it to be possible for any general con 
elusions to be drawn as to its relation to atomic structure ; w 
do not even know whether the same element can have a tetra 
hedral arrangement in some of its 4-covalent compounds am 
a plane in others. It may, however, be pointed out that ther 
is a certain structural resemblance between the two atoms whid 
are known to give the plane configuration. They both have 
similar but unusual relation to the 6-covalent atoms of the sam 
elements. The normal relation between the 4- and 6-covalen 
states of the same atom is that both have the same core, but th 
latter has four more shared electrons. Thus 

Si in [SiF G ]~ : 22 6 = (2) (8) 6, 6. 
Si in SiF 4 : 18 4 = (2) (8) 4, 4. 

So the arsenic in the active 6-covalent catechol derivative i 
40 6 = (28) 6, 6, and in the active 4-covalent sulphide 86 4 = 
(28) 4, 4. But in both the~tellurium and the platinum compound 
the 4-covalent atom with the plane configuration, while i 
necessarily has four less shared electrons than the 6-covalent 
has two more unshared (i. e. there is a change of valency in thi 
classical sense) : 

Te in TeF 6 : 58 6 = (28) (18) 6, 6. 

Te in Te(CH 3 ) 2 I 2 : 56 4 = (28) (18) 2, 4, 4. 

Pt in [Pt(NH 3 ) 2 Cl 4 ] : 86 6 = (60) (14) 6, (f. 

Pt in [Pt(NH 3 ) 2 Cl 2 ] : 84 4 = (60) (14) 2, 4, 4. 

Whether the two unshared electrons should appear as part o 
the valency group, or as an example of the ' inert pair ' (N x 
grouplet), may be disputed ; but their occurrence in the only tw( 
classes of compounds for which the plane configuration has beer 
established is remarkable. 



1HE formation of chelate compounds has already been briefly 
JL discussed (Ch. VII and VIII) and their importance in deter- 
mining the maximum covalency of elements pointed out (Ch. IX^ " 
In this chapter we shall consider the relation of their stability to 
the number and nature of the atoms which compose them, and 
the links by which they are held together. 

The possibility of the formation of closed rings by means of 
co-ordinate links was first suggested by Tschugaeff in 1907 x in 
the case of the metallic compounds of biuret and similar sub- 
stances. The idea was developed immediately afterwards by 
Werner, 2 who applied it to a very large number of compounds, 
including on the one hand the metallic derivatives of such sub- 
stances as acetylacetone, and on the other the compounds formed 
by dyes with mordants. In recent years the same ideas have 
been applied extensively by Morgan and his collaborators 3 ; the 
word chelate was suggested by Morgan 4 to describe atomic 
groups which are capable of forming rings with metallic (or other) 
atoms by means of one or two co-ordinate links. 

The methods by which the presence of chelate rings can be 
detected have already been discussed. With the metallic com- ^ 
pounds they consist mainly in showing that the metal is not 
present as a simple ion, and either that the whole molecule is 
covalent, or, if it is ionized, that the metallic atom is part 
a complex ion which includes the chelate group. In complex 
ions of type A (below, p. 289) a divalent anion such as the carbonate 
ion is proved to be covalently attached to the central atom by 
the fact that the complex gives no reactions of that anion, and 
is proved to form a ring because it must occupy two"plaees on 
the central atom in order to make up the co-ordination number. 
The evidence for the closing of a chelate ring through hydrogen 
depends on the fact that if this hydrogen atom forms a second 
(co-ordinate) link with another atom in the same molecule, it 
cannot do so with an atom in another molecule : it cannot pro- 
mote association. Since the hydrogen atom in question usually 
forms part of a hydroxyl group, so that the compound would 

1 J. pr. Chem. 75, 153 : Bar. 40, 1978, 3498. a Ber. 1908, 41, 1062. 

3 J. C. S. from 1913 onwards. 4 Ibid., 1920, 117, 1457. 

3063 TT h 

234 Chelate Kings 

normally be highly associated, the change of properties resulting 
from, chelation is considerable. On comparison with otherwise 
similar but non-chelate compounds the substance is found to be 
more volatile, more soluble in non-associated and less in associated 
1 solvents. 1 

A rather unexpected but valuable source of information as to 
the possible types of chelate rings is provided by the study of the 
structure of mordant dyes. 2 That the action of mordants is due 
to the formation of co-ordinated ring compounds with the metal 
was first pointed out by Werner, 3 who not only showed that many 
mordant dyes had structures analogous to those of compounds 
known to form such rings, but also proved that cloth mordanted 
with chromium or iron salts was actually dyed by immersion 
in a solution of a j8-diketone or a jS-ketonic ester, such as acetyl- 
acetone or acetoacetic ester. These substances are of course 
colourless, but the dyeing of the cloth is shown by the change of 
colour of the iron or chromium mordant itself. More recently 
Morgan and his collaborators have prepared and analysed a 
large number of chelate metallic compounds of a variety of 
mordant dyes (especially of the alizarine class), and have estab- 
blished their constitution. It may thus be taken as proved that 
the power of dyeing cloth mordanted with metallic salts is an 
indication that the dye is capable of forming chelate rings. This 
enables us to extend our knowledge of the possible forms of 
chelate ring by examining the structure of these dyes. 

In any catalogue of dyes there will be found a large number 
(for example, some 160 are enumerated in Schultz, Farbstoffta- 
bellen, 1914) of dyes of established constitution which can be 
mordanted with salts of polyvalent metals. Of these all but some 
half dozen contain a replaceable hydrogen atom and a donor 
atom so disposed as to be able to form a ring of either six or 
five atoms (124 of the former and 88 of the latter in Schultz's 
list) connected to the aromatic ring in the ortho-position. The 
great majority of these rings are of types already known on other , 
evidence to occur in chelate compounds. For example, the most 
important type of chelate ring from every point of view is the 

1 See Chapter VIII, p. 147. 

2 This term is used to describe those dyes which only adhere to the fibre 
after it has been treated with a salt of a polyvalent metal such as chromium 
iron or aluminium. There is another method of mordanting, by treating 
the cloth -with tannin and an antimony compound ; but the mechanism of 
this process is quite different, and so are the types of dyes to which it is 
applicable. 3 loc. at. 

Mordant Dyes 


6-ring containing two conjugate double links. This occurs in 
neariy all the chelate compounds mentioned in the preceding 
chapters. Among mordant dyes we have an immense number of 
compounds of this type. All the alizarine dyes are substitution 
products of 1-hydroxy-anthraquinone and hence can form this 
ring : l 

in which M represents one equivalent of the metal of the mor- 
dant. Among the azo-dyes it is an established principle that two 
classes are always mordant dyes : (1) those in which the first com- 
ponent (the diazotized amine) has an ortho-hydroxy-group ; 
and (2) those in which the second component is a salicylic acid 
derivative. Both of these classes can give rings of this type : 






It is possible to obtain the same ultimate structure as in (1) by 
introducing the ortho-hydroxy-group in the second component 
instead of the first, for example, by coupling a simple diazo-com- 
^5ound with a /?-naphthol or a para-substituted a-naphthol, and 
the product is always found to be a mordant dye. 

M O 


When the azo-group does not couple in the ortho-position to thev 
hydroxyl, the compound is not a mordant dye. 

Chelate rings differ from the ordinary isocyclic and hetero- 
cychc rings of organic chemistry in containing co-ordinate links, 

1 It is assumed that the link between any two carbon atoms in a benzene 
nucleus can be regarded as a double link. 

236 Chelate Rings 

and this form of link, as we have seen, is always a source of 
instability, since the products of its rupture are in general more 
stable than those formed by breaking a normal covalency. This 
comparative instability is shown by the fact that while normal 
brings with any number of atoms from three to eighteen are known, 
/ chelate rings never contain less than four and very rarely more 
than six. This limitation of size is evidently due to the effect of 
strain, to which the co-ordmate link renders these rings peculiarly 
sensitive. We may therefore consider briefly the strain theory 
of Baeyer and its later developments. 


This theory was founded on the simple assumption that the 
angle between two of the valencies of an atom has a ' natural ' 
value determined by the atomic model, and that any departure 
of the angle from this value produces a corresponding strain or 
instability in the molecule. For carbon on the tetrahedral model 
of van *t Hoff the natural angle (the angle between the lines join- 
ing the centre of a regular tetrahedron to two of its angular 
points) is 109 28'. A modification of this theory was proposed 
by Ingold, 1 to account for the fact that the instability of certain 
rings is not that required by Baeyer's theory. He pointed out 
that the tetrahedron can only be regarded as regular when the 
carbon atom is joined to four atoms of the same size, and that 
therefore the angle between the two valencies forming part of 
the ring will vary according to the nature of the two other atoms 
attached to the carbon ; if these are also carbon atoms, as in 



we may assume that the tetrahedron is regular, and that Baeyer's 
value of the angle holds good, but if they are smaller atoms, as in 



the angle will be larger. To calculate its value, Ingold adopts 
a model formed by taking four spheres of volumes proportional 
to the atomic volumes of the attached atoms, and arranging 
them so as to be in contact with one another and with an enclosed 

1 J. C. S 1921, 119, 805. A similar view was suggested qualitatively by 
Mamlock (Stereochemie, Leipzig, 1907, pp. 99, 100), and even foreshadowed 
by Wislicenus (Raumhche Anordnung der Atome, Leipzig, 1888, pp. 75-6). 

Theory of Strain 237 

sphere. This gives an irregular tetrahedron, and the angle be- 
tween any pair of valencies is that subtended at the centre of the 
enclosed sphere by the line joining the centres of the two attached 
spheres in question. In this way he calculates that the angle be- 
tween the two carbon valencies in the group 

H C- 


is 115 18'. A large amount of evidence has been brought 
forward by Ingold and others which strongly supports this 
hypothesis as a qualitative theory. But its quantitative value 
is much less certain. The difficulty which faces us as soon 
as we attempt any refinements on Baeyer's original idea is 
that of giving a definite meaning to the word strain. We may 
take it that the distortion of the orbits of the shared electrons 
from their natural positions produces a resisting force, and that 
this force or the distortion which causes it tends to weaken 
the attachment of the atoms to one another. We may also take 
it that the distortion, the resisting force, and the consequent 
weakness all increase together ; but beyond this we know noth- 
ing of the laws which relate them to one another. Moreover the 
' natural angle ' of no strain must be determined by the geometry 
of the electronic system. If we adopt Ingold's view that the 
nature of the attached groups alters the size of the angles, this 
is itself a distortion of the orbits, and must set up a resisting force 
of some kind ; this means that the distortion will be shared 
among the angles concerned, but in what proportions we do not 
know. We are therefore not justified in assuming either that 
Ingold's simple calculation of the angles from the volume rela- 
tionships of the attached groups is correct, or that the jesulting 
angles are ' strainless '. 

Hence while the existence and the importance of strain are 
undoubted, any theory can only be a rough approximation to 
the facts, and we cannot hope at present to reach quantitative 
accuracy. So long as this is recognized, the theory of strain is 
of considerable value, and it is important to compare its predic- 
tions with the experimental facts ; and for this comparison the 
chelate rings are peculiarly suitable, owing to the simplicity of} 
their rupture, which does not involve any extensive intramole- ' 
cular rearrangement. 

On the simple Baeyer theory we have certain fundamental 
values of the angles, based on the regular tetrahedron, which may 

238 Chelate Rings 

be assumed to hold not only for carbon, but also for all atoms of 
the first short period, and all other atoms in compounds in which 
they show the tetrahedral type of symmetry (see last chapter). 


For the simple angle C<( p the value is 2 tan" 1 </ 2 = 109 28'. For 


the angle C^p , if we assume that the two doubly linked tetrahedra 

have an edge in common, it is 180 tan" 1 J 2 = 125 16'. From 
these values we can calculate the strain (that is, the deflection 
from the natural angle) in rings of various sizes, both with and 
without double links. The results are given below : the strain 
is assumed to be equally distributed among the atoms of the ring, \ 
and is counted as positive when the polygonal angle is less than ' 
the natural (when the strain is ' inwards '). It is also assumed 
that no atom forms more than one double link. 

Strain per Atom of Ring. 

No. of atoms Number of double links. 

in ring. 0123 

3 +49 28' +60 0' - - 

4 +19 28' +27 22' +35 16' - 

5 + 1 28' + 7 47' +14 6' - 

-10 32' - 5 16' +0 + 5 16' 

It has long been recognized that when the strain is in this sense 
negative, the theory no longer holds, because it assumes that 
the ring lies in a plane. This gives the maximum angle of the 
polygon, and therefore the least strain when the strain is positive ; 
but when it is negative, an appropriate departure from the plane 
configuration will remove it entirely. At the same time it is 
evident from the behaviour of normal organic rings that negative 
strain is not negligible or at least connotes difficulty of formation, 
for rings of more than six atoms are comparatively rare. We 
can therefore see that, provided the strain is shared equally 
among the members of the ring, the most stable forms of ring 

\ 1 should be a saturated 5-ring and a 6-ring with two double 

it links. This is fully confirmed by experiment. 

' When an atom has a covalency of less than four, as in divalent 
oxygen or tnvalent nitrogen, the most reasonable assumption 
is that the angle between the valencies remains the same as when 
the full covalency is exerted. 

We have so far considered only atoms with a tetrahedral 
arrangement of the attached groups. With the co-ordinated 
hydrogen atom the simplest assumption would seem to be that 

Types of Chelate Rings 239 

the angle between the two valencies is 180, but we have at 
present no means of discovering whether this is actually so. 
With 6-covalent atoms the natural angle between two adjacent 
valencies is 90, and the same is true of those 4-covalent atoms 
in which the attached groups have been shown to lie in a plane. 
As we have seen, this disposition has only been established for 
two elements, 1^11iirjLUJiL.and platinum ; it is, however, possible 
that others of the heavier elements may be able in their 
4-covalent compounds to assume this form, and of this there 
is some evidence, though it is not conclusive. 1 

The size of the component atoms must also have an effect. In 
the simple theory it is assumed that they are all of the same size, 
and this is very nearly true of those important constituents of 
chelate rings carbon, nitrogen, and oxygen, of which the diameters 
according to the X-ray data are about 1-5, 1-8, and 1-3 x 10~ 8 cms. 
respectively. The heavier atoms which form part of many 
chelate rings are of course larger, but the ease with which the 
ring is formed when the metallic atom is replaced by hydrogen 
suggests that the size is not of great importance. 2 


We can classify the various kinds of chelate rings in two ways 
either by the nature of the links which hold the ring together, 
or by the number of atoms which it contains. In respect to 
the nature of the links, we can distinguish three types. 

Type A. Rings which, strictly speaking, are formed entirely 
of normal (not co-ordinate) covalencies, but only in virtue of the 
central atom having taken up one or more electrons. The ring 
is formed by the replacement by the metal of two hydrogen 
atoms in a dibasic acid (including such weakly acidic substances 
as catechol) : examples are the sulphate- and oxalato-compounds 
of Werner, such as 


0=C Ov ,0 C=O 



0=C O/ \0 

They may be called co-ordination compounds of ions, as when 
they dissociate they normally form ions, the beryllium salt above, 

1 See below, p. 244. 

2 If we can assume that the natural angle is 180 for hydrogen and 90 
for the heavier atoms, this would of course tend to compensate for the 
difference m size. 

240 Chelate Rings 

for example, giving beryllium ions and oxalate ions. Of the four 
electrons required to enable the beryllium atom to replace four 
hydrogen atoms, two are taken from the potassium, so that the 
complex is a divalent negative ion. The value of the electro- 
valency in such compounds varies widely, being in fact equal to 
the number of hydrogen atoms replaced minus the valency of the 
central atom. Thus boron needs one electron to form a dichelate 
compound of this type, while aluminium needs three in the 
trioxalato-compounds, and so on. 

Chelate rings of this type are remarkably stable, as is shown 
by the occurrence among them of 4-rings which are almost, 
and of 7- and even 8-rmgs which are quite, unknown among 
other classes of chelate compounds. 1 Two reasons may be 
given for this. The ring is held together entirely by normal 
covalencies, and so may be said to possess in some degree the 
stability of the ordinary rings of organic chemistry. Further, 
although it has the possibility of dissociating into the simpler 
ions (e. g. a complex oxalate into the metallic ion and the oxalate 
ion), the tendency of these to recombine is strengthened by the 
positive charge on the acceptor (the metallic ion) and the negative 
charge, on the donor. 

Type B. Rings with one definite co-ordinate link, in which the 
metallic (or hydrogen) atom is joined to the ring on one side by 
a normal and on the other by a co-ordinate link, as in beryllium 
acetylacetone or the enolic form of acetoacetic ester 

CH 3 -C O v /O C-CH 3 CH 3 -C C 

!^\/\ ^ 

CH Be CH : CH H . 


This is the largest and most important class. With atoms of 
which the covalency maximum is twice the valency, one chelate 
ring is formed for each valency, and a neutral molecule is pro- 
duced, in which the central atom has its maximum covalency, 
as in BeA 2 2 and A1A 8 . Owing to the stability of covalencies of 
four and six, even with atoms which can reach a higher limit, 
compounds of this kind occur also with the heavier elements of 
the second and third periodic groups, as in BaA 2 and LaA 3 , 
though these sometimes tend to increase their covalency by 
hydration (as in BaA 2 , 2F a O, in which the barium is 6-covalent) 

1 See pp. 248, 251. 

E A = radical of diketone. 

Types of Chelate Rings 241 

or by polymerization. When the valency is one more than half 
the maximum covalency, the latter is reached when all but one 
of the valencies are occupied with chelate groups ; the last 
valency must then appear as an electrovalency, and we get a salt, 
as in [BAJX and [SiA 3 ]X. 

This type of ring is less stable than type A, as is shown by its 
never containing less than five or more than six atoms. When 
the co-ordinate link breaks, the primary product must be an 
open-chain molecule such as M-0-C(CH 3 ) = CH-CO-CH 3 , 
the carbonyl group returning to its normal form, while M remains 
covalently attached to the oxygen of the hydroxyl group : the 
covalency of M diminishes by one (it loses its share of a pair of 
electrons), the process being analogous to the loss of ammonia 
from a complex ammine. But it is found that another change 
practically always follows, the remaining normal covalency of 
the metal being converted into an electrovalency : 

/ x \ 
M( ) - > M X Y - > M[X Y] 

In other words, the covalent compound changes into a salt. It 
is very rare, at any rate with the more stable types of chelate 
compounds, to find a substance in which a potentially chelate 
group is attached only by a single covalency : it is either 
attached by two to form a ring, or it is ionized. Boron, for 
example, with a valency of three and a maximum covalency of 
four, can form compounds of the type of the acetate B(O- CO- CH 3 ) 3 
non-chelated, tri-covalent and also of the type of 

CH 3 -C O-CO-CH, 

CH B< 


a neutral substance with one chelate ring and two um-covalent 
groups. A compound BA 3 , in which one of the acetylacetonyl 
groups was chelated while the other two were merely attached 
by a normal covalency, would satisfy the covalency rule, but no 
such compound exists. When the central atom is a metal 
especially a highly electropositive metal this result is to be 
expected. The metal has a strong tendency to form electro- 
valencies rather than covalencies, and this tendency can be over- 
come only when the energy of formation of the normal covalent 
link is supplemented by that of the co-ordinate link. But it is 
remarkable that the same thing should occur with an element 

242 Chelate Rings 

like boron, which always forms covalent links in preference to 

The chelate derivatives of salicylic acid might be referred 
either to type A or type B. In these compounds, which are very 
numerous, it has been shown that it is the phenolic and not the 
carboxylic hydrogen which is replaced, since they are still formed 
when the hydroxyl of the carboxyl group is replaced by hydrogen 
(aldehyde) or methoxyl (ester), but not when the phenolic 
hydrogen is replaced by methyl, in the phenol ether. Thus the 
salicylic ring can be written as 



in which the acid hydrogen is still present. In the salts of this 
univalent acid we shall then have the ionized form 


The compound thus appears as an example of type B. But the 
salt can equally well be written on type A, the central atom M 
taking an electron from the K and so replacing the two hydrogen 
atoms in the salicylic acid : 




In the present state of our knowledge we cannot decide which of 
these formulae is correct ; the difference between them is the 
difference between the two oxygen atoms in the ion of a carboxy- 
lic acid R-C<Q ; and though as the formula is here written 

the distinction is quite clear, one oxygen atom sharing two and 
the other four electrons with the carbon, it is by no means certain 
that this reaUy represents the structure of the carboxylic ion. 1 
< x See further, p. 252. 

4-Rings 243 

An argument of some force in favour of the second way of writing 
these compounds is that these complex acids are almost always 
much stronger than the simple acids from which they are derived ; 
on the other ^Jiand the chelate derivatives of salicylic ester 
cannot be written in this way. 

Type C. Rings containing two co-ordinate links, as in the 
ethylene diamine (' en ') compounds of Werner 

/NH a CH 2 

M< | '. 

\NH 2 CH 2 

Rings of this type are also formed by /?-diketones and similar 
substances with metallic atoms whose covalency is more than 
twice their valency, as with the alkali metals. 1 The metallic 
atom replaces an atom of hydrogen in one molecule of the dike- 
tone, and a second molecule is then added without replacement. 
Rings of this type are as a rule less stable than those of type 
B, because the whole molecule can break off by the rupture of the 
two co-ordinate links. 

We have now to consider the principal kinds of chelate rings 
which have been found to occur, and these are most conveniently 
classified according to the number of atoms in the ring. In order 
of importance the 6-rings come first, followed by the 5-rings. 
4-rings are comparatively scarce, and only occur under special 
conditions ; 7- and 8-rings are entirely limited to type A, and only 
very few of them are known. 


These are rare, and practically all belong to two peculiar 

(1). Complex ions containing anions of dibasic acids of the 

H O 
form TT^^X, such as the sulphate- and carbonato-compounds 

of Werner 

,0 X .-O /O\ 

M S and M C=0 . 

, X .- 
< >S< 
\CK ^ 

Some of these are remarkably stable, such as [Co(C0 3 )(NH 3 ) 4 ]Cl, 
from which silver nitrate precipitates only the chlorine, and 
barium chloride precipitates nothing. 

(2). The other established class of 4-rings consists of certain 

1 See p. 146. 


Chelate Rings 

' polynuclear ' co-ordination compounds (i. e. containing more 
than one metallic atom in the complex), such as 



A large number of these are known, 1 some of which have the 
OH replaced by NH 2 . There seems no reason to dispute Werner's 
formulation of them, and it will be noticed that the two metallic 
atoms are 6-covalent, so that the natural angle between their 
valencies is 90. This reduces the mean strain in the ring to half 
(from 4-19 28' to +9 44'). 

We have assumed, as Werner does, although the evidence is 
not conclusive, that a 4-ring of this type exists also in the poly- 
merized covalent halides of the trivalent metals, that A1 2 C1 6 for 
example is 

Ck , 

It is evident that the reason wlrj the trihahdes of the third 
periodic group are usually polymerized, while the tetrahalides 
of the fourth group are usually not, is that the former strive to 
acquire a complete octet, which the latter already possess. If the 
ring is not formed, the structure must be 
Ck /Cl 

CK \C1 ' 

which only completes the octet of one of the two aluminium 
atoms ; and in that case it is difficult to see why the polymeriza- 
tion does not proceed farther. On the other hand the 4-ring 
structure would seem to involve too great a strain for a ring with 
two co-ordinate links, unless we can suppose that an atom which 
is capable of a covalency of six can have (although as we have 
seen it does not usually do so) in its 4-covalent compounds 
a plane distribution of its valencies such as we find in tellurium 
and platinum. On this assumption the angle between the valen- 
cies of the metallic atom is 90, and the strain is halved, the ring 
being of the same kind as in the polynuclear cobalt compounds 

1 See Werner, Neuere Anschauungen, 1923, pp. 269-91. 

5-Rings 245 

mentioned above. If we extend this idea to the halogen atom as 
well, the strain vanishes entirely except in the fluorides, since 
fluorine is the only halogen for which a covalency of six is 
theoretically impossible : and the fluorides do not polymerize as 
the other halides do. This hypothesis is rather bold, and is cer- 
tainly not proved ; but it is supported by one remarkable fact. 
Boron, being in the first short period, cannot under any circum- 
stances be 6-covalent, and so the natural angle of its valencies 
must always be the tetrahedral angle of 109 28' ; a 4-rmg such as 



would therefore be impossible, and this may be the reason why 
boron, which is the only element in the third group incapable 
of a covalency of six, is also the only element in that group to 
form trihalides which are not polymerized, and are correspond- 
ingly volatile. 


These occur in all three types A, B, and C. Type A is especially 
common in the double oxalates or oxalato-compounds, and in 
the numerous derivatives of catechol, such as the optically active 
arsenic compound 

Type B. The low boiling-point of catechol itself as compared 
with its meta and para isomers indicates that it is to a consider- 
able extent chelated . Other examples are the metallic derivatives 
of the benzoin of phenyl-glyoxal 

HC NH, NH 2 -CH 2 


M M 

and certain derivatives of glycocoll, especially the copper com- 


f , 

o=c o/ \ o oo 

whose properties show it to be covalent. Another series of com- 
pounds which must form rings of this type is found among 
mordant dyes. Nearly all the mordant dyes which cannot form 

246 Chelate Rings 

chelate 6-rings of the kinds described in the next section are 
of the type 

in which B is oxygen (rarely sulphur), D nitrogen (rarely 
carbon), and A and A' are hydroxyl (rarely NH 2 ). We cannot 
suppose that chelation takes place between B and A (which 
would give a 6-ring), because compounds in which a second ring 
is attached to the benzene nucleus in the meta position are almost 
if not quite unknown, and as all these dyes contain a hydroxyl 
or NH 2 at A', it is to be presumed that the chelate ring closes 
between B and A', giving a 5-ring of the type 

M< I, 
^B C 

where A' is nearly always oxygen, and B is also oxygen (or 

Other 5-rings are found in the hydroxamic acids 

/O NH 

M \ 



according to Werner : in the ' cupferron ' compounds 


and presumably to some extent in the ortho-halogen-phenols 

/x -\ 


as these are definitely though not very strongly abnormal in 
boiling-points and solubilities. 

Type C. This includes the numerous co-ordination compounds 
in which a molecule of ethylene diamine replaces two of ammonia, 
such as those with which Werner first established the optical 
activity of molecules of the octahedral type. These compounds 



are especially prevalent among the transition elements, as is to be 
expected from the strong affinity of these elements for ammonia. 
A similar ring is formed 1 by the ethers of thioglycol, 

for example with copper. 

R \ 
CL )S-CH 2 

/ c < 
CK >S-CH 2 


It will be noticed that the majority of chelate 5-rings have 
no double links, owing to the fact that the reduced 5-rmg has 
the least strain. 


These are by far the most numerous, and the great majority of 
them belong to one class, that in which there are two conjugate 
double links 

~~ Sx, 

and in consequence on the simple Baeyer theory it is possible 
to have no strain. Before dealing with this, the most impor- 
tant of all the classes of chelate compounds, we may consider 
some other kinds of chelate 6-rings, although these are com- 
paratively rare. 

Of type A are the malonato-compounds, for example 


,O C 



which has been resolved into its optical antimers. Another group 
of compounds which essentially belongs to this type occurs in 
the complex acetates, which will be discussed later. 

Of type C are the trimethylene diamine compounds of Werner 
containing the ring 

/NH 2 -CH 2V 

>CH 2 

which are formed by cobalt, nickel, and similar elements. It is 

remarkable that while 1 : 2 and 1 : 3 diamines react with such 

1 Tschugaeff, Ber. 1908, 41, 2222. 

248 Chelate Rings 

elements with almost equal ease 1 to form 5- and 6-rings re- 
spectively, it is impossible to form 7- or 8-rings by the use of 
1 : 4 and 1 : 5 diamines. These last give 2 amorphous compounds 
in which probably a series of metallic atoms are linked in open 
chains through diamine molecules, as in 

We should expect to find among chelate as we do among normal 
rings that the stability was less when there were more than six 
atoms in the ring, but the entire absence of rings with more than 
six atoms in any chelate compounds except those of type A 
could hardly have been anticipated. 


The greater number of known chelate compounds contain 
6-rings of type B (with one co-ordinate link), having two double 
links in the ring. The atoms forming the ring (other than the 
metal or hydrogen atom) may be carbon, nitrogen, and oxygen ; 
for obvious reasons the two atoms united to the metal will not 
be carbon. According to the nature of these atoms we may 
distinguish at least six classes of rings, of which the more im- 
portant representatives are enumerated below. 

/O Cx /O NX X 0=N\ 

I. M\ >C II. M< >C III. M< >C 

X 0=C / x o=C / X O C^ 

/o NX /oc^ /O-NX 

IV. M^ ^>C V. M<^ J>C VI. M<^ ^>N. 

x /N=C N=N N=C 

1 An interesting proof that among saturated rings the five are more 
stable than the six has recently been given by Mann and Pope (Nature, 
1927, 119, 851 : Mann, J. C. S. 1927, 1224). They prepared the mono- 
chelate compound of platinic chloride and Oj8y-triaminopropane. Accord- 
ing as the ring is formed through the a and /3 or the a and y amino-groups 
it will have five or six members . 

Cl ,NH 2 CH 2 Cl /NH 2 CH, 

CL /| CK / \ 

XS I ) Pt * CHNH 2 

Cl/ | \NH 2 CH-CH 2 -NH 2 CK \ / 

Cl * Cl \NH 2 CH 2 

a-j8 : 5-ring. a-y : 0-ring. 

The first of these has a centre of asymmetry in the /J-carbon atom (marked 
with an asterisk) : the second is symmetrical. The product was shown to 
have the first formula by resolution into its optical antimers. Thus the 
5-nng is formed in preference to the 6. 2 Tschugaeff, Ber. 1900, 39, 3190. 

6-Rings with two Double Links 249 

Class I. -keto-esters (acetoacetic ester) : /J-diketones (acetyl- 
acetone) : a-dicarboxylic esters (malonic) : salicylic acid, ester, 
and aldehyde : 1-hyd.roxy-naphtho- and anthraquinone : ortho- 
hydroxy-acetophenone. These are some of the more familiar 
examples : they have been sufficiently discussed already. 

Class II. Ortho-qumone oximes : ortho-nitrophenol : mon- 
oximes of a-diketones : oximes of a-ketonic esters. 

Class III. Chelate compounds containing this ring are formed 
by nitroso--naphthol, and also with the alkali metals by pseudo- 
indoxyl derivatives. The same grouping is found in indigo and 
in the y-pyridones, and some of the peculiarities of these com- 
pounds may be due to the formation of chelate rings. 

Class IV. This occurs in the dioximes of a-diketones, as in 
the well-known dimethyl-glyoxime compound used for the quan- 
titative estimation of nickel. Tschugaeff, who discovered this 
reaction, originally assumed that the metal was attached to the 
oxygen of the second as well as to that of the first oxime group ; 
this would give a very improbable 7-ring. Later he showed that 
it was more likely to be joined to the nitrogen of the second oxime 
group, the structure being 

CH 3 -C=N-0 X CH 3 -C=N-CK 

,M 1 >M, 

CH 3 -C=N^ and not CH 3 -C=N-0^ 


and so forming a 6-ring. He confirmed this by showing that 
similar chelate compounds are formed by the oxime of a-acetyl 


Class V. This is present in the compounds of mordants with 
azo-dyes having a hydroxyl in the ortho-position to the azo- 
group. Certain mordant dyes derived from hydroxy-pyrazolone 
also belong to this class. The same ring (except for a shift in the 
position of the double links) occurs in one of the stereoisomers 
of the hydrazone of glyoxylic ester and of camphor quinone. 1 

Class VI. This occurs in the metallic (nickel, copper, palladium) 

1 Taylor and Ewbank, J. C. S. 1926, 2821. 


250 Chelate Rings 

derivatives obtained 1 from nitrosoguanidine, presumably acting 
in the hydroxylic form : 

N=N-OH /N=Nv 

H 2 N-C< > H 2 N-C/ >0 

^NH ^N->M/ 


Tschugaeff gives a slightly different formula, with an imine group 
outside the ring, and only one double link inside ; but for the 
stereochemical reasons given above, this seems less probable. 

All these five classes contain the 6-nng with two double links 
(if we count the link in the aromatic nucleus as double) and no 
doubt owe their stability to the absence of strain in such a ring. 2 

Compounds of class I (free from nitrogen) are peculiar in that 
the organic substances which form chelate rings of this type 
most easily are also those which show a definite acidity 3 : 
roughly speaking the two properties seem to go together. It is 
clear that neither of them can be the direct result of the other, 
since chelation and lomzation are two alternative reactions 

possible for the enolic form 


' (U^i 

_ - s 

I - t * \ [-f-H-J- J . , 

1 Thiele, Ann. 1898, 273, 183 : Tschugaeff, Ber. 1906, 39, 8388. 

2 Prof. T. S. Moore has, however, pointed out to me that although the 
' natural angles ' add up to 720, as do those of a hexagon, the ring is not 
symmetrical owing to the positions of the double links, and if the angles 
are all to be strainless the sides cannot be equal : thus in class V above, 
if the other five sides are of equal length, the side M O will be 1-49 
times as long. If the six sides are all equal (i. e. if the six atoms of the 
ring all have the same diameter), the angles will all be 120, and so the 
strain on each doubly linked atom will be + 5 16', as in Kekuld's formula 
for benzene, and that on each of the two which are not doubly linked 
will be,if the ring lies in a plane 10 82'. This suggests that chelate rings 
of this type should be especially stable when M is a large atom, and such 
compounds no doubt are stable, but so are those with small atoms such 
as beryllium. It will be noticed that this form of ring (apart from 
the co-ordinate link) also occurs in the ortho-qumones. In the para- 
quinones the double links are symmetrically disposed, and hence there is no 
strain if all the sides are equal. This may explain the greater stability of 

3 The evidence for the acidity of these compounds needs, however, to be 

-C-CH 2 -C- -C=CH-C- 

7 -Rings and 8-Rings 251 

Other things being equal, the occurrence of one of these reactions 
will diminish that of the other, as is shown by the fact that 
compounds containing the -C(OH)=CH-CO- group in such a 
position that chelation is impossible for steric reasons are unusu- 
ally acidic. 1 The simultaneous occurrence of these reactions is 
no doubt due to two common causes. Firstly, any structure 
which tends to enolization will promote both. Secondly, the 
relative positions of the two oxygen atoms which are favourable 
to chelation are also those which promote ionization. As the 
ring in order to be stable with the two double links must contain 
six atoms, the second oxygen atom must be in the /3-position 
with respect to the first. This gives us in the enolic form a group- 
ing which differs from a carboxyl group only in the interposition 
of a -C=C- group : 

_C=CH-C- C- 

On any form of the theory of alternating polarity it is to be 
expected that the acidifying influence of the carbonyl on the 
hydroxyl, which is so marked in the carboxyhc acids, will be 
transmitted through this grouping. 


Only a very few chelate rings of more than six atoms have 
been observed, and they all belong to type A. Duff has shown 2 
that cobalt can form 6-covalent compounds in which two 
of the positions are occupied by the anion of a jS-dicarboxylic 
acid such as succinic, dibromosuccinic, maleic, itaconic, &c. This 
involves the presence of a 7-ring, as in 



NO fl 
CHBr-C 0'' 

scrutinized with some care The ordinary equations for ionic equilibria, 
for example, in the hydrolysis of salts, no longer hold when the base is 
capable of forming non-ionized complexes with the acid. 

1 For example, ethyl cyclobutenolone carboxylate (Taylor and Ewbank, 
loc. at.) and dimethyl dihydro-resorcmol and the /?-diketo-cyclopentane 
derivatives. (See Bennett, Chem. and Ind. 1926, 960.) 

2 J. C. S. 1921, 119, 885. 

252 Chelate Rings 

Previously Price and Brazier had found 1 that sulphonyl- 
diacetic acid gave similar chelate compounds such as 

/CH 2 -C-0\ 
2 S< >Co(en) 2 

X CH 2 -C-CK 

which thus contains an 8-ring. 

The molecular weights of these substances have not been 
determined, nor their iomzation measured ; but there seems 
little doubt that they are correctly formulated. Their occur- 
rence is peculiarly interesting in view of the failure of all attempts 
to obtain such 7- or 8-rings of other types. 

Co-ordination and the Carboxyl Group. 

The question whether the carboxyl group can form chelate 
rings is one of some interest, and may be considered here. The 
precise structure of this group has been much discussed. In 
many ways the C =0 in an acid does not behave like an ordinary 
carbonyl group. 2 It does not give the carbonyl reactions with 
phenyl hydrazine or hydroxylamine ; it is much less easily re- 
duced ; its refractive power 3 and its parachor 4 are less than we 
should expect. Two adjacent carbonyls in the a-diketones give 
the compound an intense yellow colour, as we see in diacetyl, 
glyoxal, and benzil ; but pyruvic and oxalic acids are colourless. 
These and similar reasons have led to the belief that the hydrogen 
in the carboxyl group is in some way attached to both oxygen 
atoms, which is commonly expressed by saying that it is co- 
ordinated with them. It is, however, to be observed that most 
of the above-mentioned peculiarities are shared by the esters, 
and these must have some other explanation, since co-ordination 
in this sense is not possible with the esters. 

Whatever may be the explanation of these facts, it is obviously 
worth while to inquire into the evidence for co-ordination in the 
carboxylic acids and their metallic derivatives. On general 
grounds it might be expected to occur. The hydrogen of a 
hydroxyl group, when it is not too acidic, is well known to be 
able to act as an acceptor, and so is the metallic atom which 

1 J. C. S., 1915, 107, 1367. a See Smedley, J. C. S. 1909, 95, 231. 

3 Bruhl, Ber. 1907, 40, 896. 4 See p. 126. 

The Carboxyl Group 253 

replaces it. The carbonyl group readily acts as a donor : in 
fact these two groups are the cause of the ring-closure in the 
compounds we have just been considering. The abnormal pro- 
perties of the carbonyl group in the free acids lend further 
support to the idea of ring formation. Nevertheless there is 
strong evidence that rings of the type of 

H or R 

cannot exist, and that while the two groups OH and C=O 
are very ready to form a co-ordinate link as acceptor and donor 
respectively, they* cannot do so within the limits of a single car- 
boxyl group, because the strain in the resulting 4-nng would 
be too great : there is no example of a ring of this size and this 
type, consisting solely of elements with a covalency maximum less 
than six. 

Consider first the behaviour of acetic acid. We have already 
seen that a group capable of forming a chelate ring with a 
metallic atom can almost always do so with hydrogen, so that 
if the acetates (and the salts of carboxylic acids in general) can 
form a ring 

T?-.r M 


acetic acid should form a similar ring 

The properties which this compound would have we know already 
from the analogy of such substances as acetoacetic ester and 
ortho-nitrophenol. It would have a relatively low boiling- 
point, and the association which the hydroxyl group normally 
causes would be suppressed. The actual properties of acetic 
acid are the opposite of this. Its boiling-point is 40 higher 
than that of the alcohol with the same number of carbon atoms, 
and 60 higher than that of its methyl ester. The following table 
shows the effect of methylation of the hydroxyl on the boiling- 
points of these compounds : 

Boihng-poinl of R OH R-OCH 3 Diff. 

Ortho-nitrophenol .... 214 265 +51 

Para-mtrophenol .... 295 259 -30 

Acetic acid ...... 118 58 -60 

Benzoicacid ..... 249 199 -50 

254 Chelate Groups 

Acetic acid can be shown to be associated, not only in the pure 
liquid and in non-associated solvents, but even in the vapour. 
Its behaviour is exactly parallel to that of para-nitrophenol : 
it is the behaviour of a substance containing in the molecule 
a donor and an acceptor, both active, but prevented by their 
position from reacting with one another, in the meta and para 
substituted phenols because they are too far apart, and in the 
carboxyhc acids because they are too near : so that the co- 
ordinate link can only be formed between two molecules, and 
polymerization (association) results. 

In the simple acetates again we find no evidence of co-ordina- 
tion. They are not always salts : they are sometimes covalent 
(i. e. they behave like esters), but that is a very different matter. 
They follow the type of the halides rather than that of, say, the 
acetylacetonates. Thus boron forms B(O CO-CH 3 ) 3 , which does 
not behave as a salt, but rather like the trichloride ; on the 
analogy of the acetylacetonate it should form a salt 

A\J \jJLJLo * 


Lowry and French have shown * that the cupric derivatives of 
the higher fatty acids behave as non-polar compounds, and are 
more soluble in non-hydroxylic solvents than in water. They 
conclude that these are chelate compounds, in which the copper 
forms part of two 4-rings. But their evidence does not prove 
anything more than that these copper derivatives can exist in 
a covalent form 


& & 

analogous to the boron compound. 

The only acetates whose formulae indicate that the carboxyl 
group occupies two co-ordination positions have structures which 
allow of the two oxygen atoms of each carboxyl group attach- 
ing themselves to two different atoms, so as to form a ring of 
more than four members. One example is the ' basic ' beryllium 
acetate with its analogues. In these compounds the carbonyl 
oxygen does not join itself to the metallic atom attached to the 

1 Proc. Roy. Soc. 1924, 106, 489. 

The Carboxyl Group 255 

other oxygen of the same carboxyl but to another one, and a 
6-ring is formed through the central oxygen 


A similar arrangement must occur in the complex iron and 
chromium derivatives of the carboxylic acids. It is remarkable 
that iron never forms simple salts of the type Fe[O CO R] 3 at 
all, 1 but invariably complex compounds, and that these always 
have more than one, and nearly always three, iron atoms in 
the molecule. Thus the blood-red solution obtained on testing 
for an acetate with ferric chloride contains the salt 

[Fe 3 (OH) 2 (0 CO-CH 3 ) 6 ]0 CO CH 3 . 

Analogous chromium compounds occur, and even mixed deriva- 
tives, in which one or two of the iron atoms are replaced by 
chromium. The structure of these compounds is obscure, but 
it is at least clear that the co-ordination of the C=O of the 
carboxyl group is only possible when there is a second metallic 
atom in the molecule, so that a ring of more than four atoms 
can be formed. 

1 Weinland, Komplexvcrbmdungcn, p. 849. 



WE have already considered the relation of the periodic 
classification to the atomic structure (Ch. Ill, pp. 38-47), 
and the bearing of this on the chemical characteristics of the 
periodic groups (Ch. V) and on the tendency of the elements to 
ionize (Ch. VI, p. 104). The detailed application to the indi- 
vidual elements and their compounds of the principles of valency 
at which we have arrived will be the subject of the next volume. 
It may, however, be useful at this point, even at the cost of 
some repetition and some anticipation, to give a brief account, 
in the light of what has already been said, of the more important 
valency relations of the several groups of the periodic table. 

The form of periodic table most suitable for this purpose 
has already been given (Ch. V, p. 75) and its relation to the 
Bohr theory discussed. In this table, which is essentially that of 
Mendele'eff, the elements are divided into nine groups (O VIII), 
all but the first and last of which consist of two typical elements 
and two subgroups A and B. Generally speaking, in the Nth 
group the members of the A subgroup contain N more electrons 
than the preceding inert gas, while those of the B subgroup have 
8 N electrons less than the next following inert gas. Hence in 
the first two periods, in which each inert gas has 8 electrons more 
than its predecessor, the same element represents the A and B 
subgroup : these are the typical elements. An obvious modifica- 
tion of this scheme is required in the rare earth period, owing to 
the expansion of the antepenultimate fourth quantum group of 
electrons from 18 to 82. The conventional name of eighth group 
is retained for the three transitional triads, although this group 
should strictly be divided into three, the eighth group proper 
(iron, ruthenium, osmium), a ninth group (cobalt, rhodium, 
iridium), and a tenth group (nickel, palladium, platinum). 

As it will often be necessary in this chapter to give numerical 
values of the ' valency ' of elements, the reader may be reminded 
that this term is used in the sense defined in the last section of 
Chapter X (p. 182), as equal to the diminution in the number of 
unshared electrons in the atom caused by its state of combina- 
tion. This value is not affected by co-ordination or complex 

Group : Inert Gases 257 

formation when the atom in question acts as an acceptor, nor in 
the case of a cation by the conversion of a covalency into an 
electrovalency (ionization) ; in the oxy-compounds it is the 
same whether we regard the atom as joined to a single oxygen 
atom by a double link or by a co-ordinate link. Thus the valency 
of iron is three in 

/Cl Ck yCK /Cl 

Fef Cl , in >Fe< >Fe< , 

\ci cr x cr x ci 

in K 3 [Fe(CN) 6 ], and in [Fe]Cl 3 ; and that of sulphur is 6 in 

and in 0=sC . 


He 2 Ne 10 ' A 18 Kr 36 X 54 Em 86. 

Only the first of these calls for any comment, or can be said to 
have any chemical properties. The spectrum of neutral helium 
consists of two apparently unrelated spectra, known as the 
parhelium and orthohelium spectra ; the latter, since its inten- 
sity can be increased by appropriate electrical excitation, is 
evidently due to a second (excited and metastable) state of the 
neutral atom. Bohr showed that whereas the stable parhelium 
atom has both its electrons in Ij orbits, the ortho-form has the 
second electron in a 2 orbit, from which, by the correspondence 
principle (p. 34), it cannot return to the more stable 1 1 orbit 
directly, but only by collision. Hence it is possible by suitable 
electrical treatment to convert a considerable proportion of the 
helium into this form. Orthohelium, having one electron much 
more loosely held than the other, should be a univalent element 
resembling hydrogen in its properties, and hence with analogies 
to the alkali metals; its spectrum is similar to that of lithium. 
Various attempts have been made to induce excited helium to 
enter into chemical combination, and it has been proved to form 
a fairly stable solid compound with tungsten (apparently WHe 2 ), 
and probably at low temperatures very unstable solid compounds 
with iodine, sulphur, and phosphorus. It also forms a gaseous 
compound with mercury of uncertain composition (we should 
expect HgHe 2 ), and there is some reason to think that it can 
polymerize to He 2 . 

306* L l 



Hydrogen may be included either in group I or group VII : 
in either case it is so peculiar as to need special treatment. It 
occurs in combination in five forms : (1) as a cation [H] + ; (2) as 
an anion [H]~ ; (8) as a uni-covalent atom H , attached by two 
shared electrons ; (4) rarely in a covalent form attached by a 
single shared electron ; (5) as a co-ordinated divalent atom H<-. 

(1) The simple hydrogen ion, consisting of a single proton, is 
probably rare, most acids being covalent in the pure state, and 
the ion in dissociating solvents being almost invariably solvated, 
and therefore in condition (3) or (5). 

(2) The negative hydrogen ion occurs (p. .64) in the hydrides 
of the alkali and alkaline earth metals. 

(3) The marked tendency of hydrogen to pass from the 
ionized to the covalent state, to which the weakness of weak acids 
is due, is to be expected on the Fajans theory, since hydrogen is 
the extreme case of a small cation. It may also be explained, as 
Lewis suggests, as being due to the fact that hydrogen alone 
among cations is satisfied with the pair of shared electrons which 
it obtains by forming a co valency with its anion. 

(4) The peculiarities which on physical grounds we should 
expect hydrogen to show, owing to its core consisting of a single 
proton with no attached electrons, are comparatively little 
apparent in its chemical behaviour ; but there is reason to 
think (p. 102) that it is the one element which can be covalently 
linked by means of a single shared electron ; this form of link is 
only known to occur between hydrogen and hydrogen (as in 
H 2 + ) or between hydrogen and boron, and is always very unstable. 

(5) The evidence for the existence of co-ordinated 2-covalent 
hydrogen has been discussed (p. 72) ; it can only act in this 
way as an acceptor when it is already united to a suitable atom, 
usually either oxygen or fluorine. 

Group I : Elements other than Hydrogen 
These elements, with their atomic numbers and atomic 
volumes (in the elementary state) are as follows : 

Li 3 Nail K19 Rb87 Cs 55 (87) A 

11-8 23-7 45-3 56-0 70-7 

Cu29 Ag47 Au79 B 

7-1 10-3 10-2 

Hydrogen : Alkali Metals 259 

Characteristic structures : A : (C) (8) 1 

B : (C) (18) 1 

In these structures the symbol (C) stands for an inner core of 
completed electronic groups ; in lithium of course the structure 
is (2) 1. 

The typical elements are very closely related to the A subgroup; 
the resemblance of the B subgroup amounts to little more than 
the power of forming univalent cations (copper and gold very 
unwillingly). The enormous difference in atomic volume be- 
tween the alkali metals and the elements of subgroup B is of 
great importance. The much greater size of the former is a sign 
that their valency electrons are in a much weaker field than those 
of the latter, or in other words, that the group of 8 electrons is . 
much more efficient (in proportion to its number) in screening 
the outer electrons from the field of the nucleus than the group 
of 18. In the ions, where the valency electrons are removed, the 
difference is much less 1 but it is in the same direction. This 
difference in the external field, and hence in the size, is the cause 
of the greater tendency of the B elements of all the earlier 
periodic groups to form covalent compounds. 

Group I : Typical Elements and Subgroup A : Alkali Metals 

The properties of these elements, are mainly governed by a 
strong tendency to ionization, since by the loss of single electron 
the atom can assume the stable structure of an inert gas. Such 
salts as the halides are always ionized, even in the solid state. 
The covalent condition is more readily assumed by the ion than 
by the neutral atom, and almost the only stable examples of it 
are found among the hydrated salts. These illustrate a tendency 
characteristic of every group of metals, that the lightest members, 
although the maximum number of water molecules that they 
can take up is smaller than with the heavier (according to the 
covalency rule), reach this maximum with greater ease. This 
agrees with Fajans' theory, of which the alkali metals, with their 
large size and their single charge, are striking examples : the 
formation of covalent links is excessively difficult for all but the 
smallest members. Accordingly we find that the salts of lithium 
are nearly all hydrated, and most of those of sodium, while 

1 The ' volume ' of an ion is not a fixed quantity, but varies with the nature 
of the other ion present, and in crystals with the nature of the lattice, so that 
it is of little use to give numerical values. 

260 Group I 

those of potassium are usually, and those of rubidium and 
especially caesium almost invariably anhydrous. Covalent com- 
pounds of neutral atoms of this series are rare ; they are 
found in the uni-covalent alkaline alkyls and aryls of Schlenk 
(p. 154) such as sodium methyl Na-CH 3 and sodium phenyl 
Na-C 6 H 5 (sodium benzyl however is a salt Na[CH 2 -C 6 H 6 ]), 
which are very unstable, being spontaneously inflammable in air. 
The covalent alkaline atom is more stable when it attains by 
co-ordination a covalency of four or six : this occurs in the 
chelate compounds of /?-diketones and similar substances (p. 145), 
among which compounds of 4-covalent lithium, sodium and 
potassium, and of 6-covalent sodium and potassium are known. 

Subgroup IB: Copper, Silver, Gold 

These elements resemble the alkali metals in having one 
electron more easily removed than the rest, but differ from them 
in that the next electronic group contains 18 electrons instead 
of 8. Thus they are all capable of a valency of one : but the 18 
group is less stable than the 8, and it is possible under some 
conditions to utilize some of its electrons for valency purposes, 
so that we find the higher valencies of 2 in copper and 3 in gold. 
We may consider first the univalent compounds, in which alone 
these elements are comparable with the alkali metals. The small 
size of their ions makes them (and especially copper, the smallest 
of them) much more ready than the alkali metals to form cova- 
lent links. Although the halides are ionized in water so far as 
they dissolve, and in the fused state (cuprous chloride only 
partially), the cuprous have non-ionic lattices in the crystals, 
and so does silver iodide at the ordinary temperature, and 
cuprous chloride is bimolecular (and therefore covalent) in the 
vapour. In the same way these elements all have a marked 
tendency to form complex ions, as in K 2 [CuCl 3 ], [Ag(NH 3 ) 2 ]Cl, 
and K[Au(CN) 2 ]. The value of the covalency in these complexes 
seldom exceeds 3 and never, so far as is known, 4. 

The existence of cuprous salts is limited by the possibility of 
the reaction 

2 Cu+ = Cu ++ + Cu, 

the equilibrium between the two ions being much in favour of 
the cupric (the cuprous ion has been shown to be Cu + and not 
Cu a ++ ). Thus a cuprous salt readily soluble in water without 
forming complexes, and so giving a high concentration of cuprous 

Copper, Silver, Gold 261 

ions, would decompose into the cupric salt and metallic copper : 
this happens with cuprous sulphate, which can be made in the 
absence of water (from cuprous oxide and dimethyl sulphate), 
but is at once decomposed by water with separation of copper. 
Similarly cuprous nitrate, which cannot be obtained as such, can 
exist in the complex [Cu(CH 3 -CN) 4 ]NO 3 . The stable cuprous 
compounds, such as the halides, are those which are practically 
insoluble in water, and only dissolve in presence of something 
(such as hydrochloric acid, soluble chlorides, or ammonia) with 
which they can form complexes. In the same way the aurous 
ion can only exist in very small concentration, and the salts 
readily pass into auric compounds and metallic gold. The 
stability of the silver ion, which is unique among the univalent 
ions of this subgroup, is no doubt due to the fact that the silver 
atom cannot lose (or share) more than one electron, or, as we 
should ordinarily say, that there is no higher state of oxidation 
into which it can pass. 

The occurrence of higher valencies among these elements is 
due to the weakness of the electronic group of 18 as the outer 
group in a univalent ion. In copper, one of the electrons of this 
group can be ionized or shared, in silver none, and in gold two 
can be shared but not ionized without great difficulty : there is 
no satisfactory proof of the existence of the auric ion Au +++ . 
Why there is this difference between the three elements we do 
not know. The spectroscopic evidence shows that the stability 
in the neutral atom of a penultimate group of more than eight 
electrons is greater when it is in the fourth quantum group (in 
the series Nb Ag) than when it is in the third (Ti Cu) or the 
fifth (Ta Au). 1 This is not an explanation of the difference 
between copper, silver and gold, but it shows that it is part of a 
more general phenomenon. The explanation will no doubt come 
when the dynamics of the atom are more fully understood. With 
the breaking down of the 18 group the properties associated with 
imperfect groups in the core appear, the colour and the para- 

The cupric compounds should be compared not with those of 
the alkali metals, but with those of the divalent transition 
elements such as nickel, or, apart from their transitional proper- 
ties, with those of zinc. Like the latter, they are distinguished 
from the alkaline earth compounds by their much stronger 
tendency to form covalent compounds and complex ions. This 
1 See list of atomic structures, p. 49. 

262 Group II 

is explained by the small size and double charge of the ion. 
Among the neutral compounds are those of the ^8-diketones and 
j8-ketoesters, which have recently (see p. 226) been shown to be 
optically active ; of the numerous complex ions the best known 
are those of the cuprammonium salts [Cu(NH 3 ) 4 ] X 2 . It is re- 
markable (and unexplained) that compounds with a covalency 
of more than four, although they are known, are comparatively 
rare, much rarer than with magnesium or calcium. 

The auric compounds are all covalent ; auric chloride is 
practically not ionized, though it dissolves in hydrochloric acid 
to give the very stable auric acid H[AuCl 4 ]. Here also, as with 
the cupric compounds, although covalencies of 5 and 6 are known, 
they are much less common than those of 8 and 4. 


Elements and Atomic Volumes 

Ca20 SrS8 Ba56 Ra88 A : (C) (8) 2 
Be 4 Mgl2 25-4 35-1 86-7 
4-92 14-0 

Zn 80 Cd 48 Hg 80 B : (C) (18) 2. 

9-5 18-0 14-1 

The contrast between the subgroups is less marked than in 
group I. In the A subgroup the core is still unalterable, and of 
the number of an inert gas ; the expansion of the penultimate 
group which occurs in the transition elements has not yet begun. 
In the B subgroup the nuclear charge (which is now two units 
more than corresponds to the core, whereas in I B it was only 
one more) holds the 18 group so firmly that it is never broken 
into either by ionization or sharing. Thus both subgroups have 
unalterable cores and constant valency. 

We still, however, have the outermost electrons in the atoms 
of the B subgroup moving in a stronger field than in those of the 
A, with a consequent diminution of atomic volume. Accordingly 
the tendency is much stronger to ionization in A, and to complex 
formation in B. This is illustrated by the electrode potentials : 
Be Mg Ca Sr Ba 

? -254? -2-56 -277 -28 

Zn Cd Hg 

-0-49 -0-40 +0-75 

The ionization tendency in the alkaline earth metals calcium, 

Typical and A Elements 263 

strontium and barium (and radium, so far as we know) is so 
strong that it determines most of their behaviour, as it does with 
the alkali metals. Of the typical elements, berjdlium, as we should 
expect from its abnormally small volume, resembles the B rather 
than the A subgroup ; magnesium has affinities with both. 

There are indications that the normal covalency is in the A 
subgroup 6 rather than 4, and in the B subgroup 4 rather than 6. 

Group II : Typical Elements and Subgroup A : Beryllium, 
Magnesium, and the Alkaline Earth Metals 

Beryllium, owing to the small size of its atom, is very different 
from the other elements. It is on the limit of lonization. Its 
chloride, though ionized in water, is a poor conductor in the 
fused state ; its oxide, unlike those of magnesium and calcium, 
has a non-ionized lattice. The beryllium ion has a strong ten- 
dency to combine with four molecules of water or ammonia ; 
it forms complexes with the greatest readiness, the oxalate being 
apparently an auto-complex Be[Be(C 2 O 4 ) 2 ], while the normal 
acetate Be[0-CO-CH 3 ] 2 is unstable and easily changes into the 
' basic ' acetate Be 4 O(O-CO-CH 3 ) 6 , a purely covalent compound. 

Magnesium has much more resemblance to the alkaline earth 
metals than beryllium. It has some tendency to complex 
formation, as is shown by the cationic mobility ratio of mag- 
nesium sulphate, which changes from 40 in 0-05 molar to 0-26 
in 1 -molar solution. It usually occurs as the ion, which readily 
takes up 6 molecules of water. On the other hand it assumes the 
covalent form in the Grignard reagent, which has been shown to 
contain normally in the solid state two molecules of ether, so 
that it no doubt has the structure 

Et,0\ Alk 

The remaining elements, calcium, strontium, barium and 
radium, form a very well-marked series, with a much smaller 
tendency to form complexes, which is perceptible m the lighter 
members, but falls off as the atomic number increases, as does 
also the tendency to hydration. 

Subgroup II B : Zinc, Cadmium, Mercury 

These elements are uniformly divalent (the mercurous ion is 
only an apparent exception), having an unalterable core two less 
than the atomic number both in the ionized and in the covalent 

264 Group II, Subgroup B 

compounds. The small size of the ions, together with theii 
double charge, makes them very ready to pass into the covalenl 
state. The halides, for example, have much less of the charactei 
of salts than those of the alkaline earths ; they are more volatile 
and more soluble in organic solvents, and their conductivities 
in the fused state are low, those of the mercuric halides very low. 
The same preference for the covalent state is shown in water ; 
zinc salts form complexes readily, cadmium salts with unparal- 
leled ease, and mercuric salts, although they do not form auto- 
complexes, are largely present in the un-ionized state. 

Mercury occupies a unique position among the metals. It 
readily forms covalent links of great stability with a variety of 
elements, especially the halogens, oxygen, nitrogen, and carbon ; 
far more ' organic ' compounds are known of mercury than of all 
the other metals together. Its stability in the covalent state is 
shown most conclusively in the mercurous ion, which has been 
proved by a variety of methods to be diatomic, consisting of 
two atoms which have each lost one and shared the other elec- 
tron. The mercurous compounds seem to be confined to those 
in which the metal is attached to a halogen or to oxygen (oxide 
and salts of strong oxy-acids), and in this state the metal never 
seems to have a covalency of more than two. The mercuric 
compounds show a further peculiarity. Not only do they ionize 
to a very minute extent (except those of the strong oxy-acids), 
but unlike the cadmium compounds they have very little 
tendency to form auto-complexes : mercury is for some reason 
far more stable with a covalency of two, and far less ready to 
increase it to four, than any other metal. This may explain the 
fact that mercuric salts are almost invariably anhydrous. 


Elements and Atomic Volumes 

Sc 21 Y 89 La 57 Ce 58 Pr 59 .... Lu 71 Ac 89 

B5 A113 116 22-5 20-0 21-8 
4-11 10-2 Ga31 In 49 T181 

14-9 15-5 17-3. 

Characteristic groupings : 

A:(C)(8+1) 2. B:(C)(18) 2, 1. 

The contrast between the subgroups is still less in this group, 
and the typical elements resemble the B subgroup more ; the 

Group III : Boron, Aluminium 265 

18 group of electrons in subgroup B attains a greater stability 
as the number of valency electrons (and so the excess of the 
nuclear charge) increases. This can be seen from the much 
smaller differences in atomic volume. 

We find for the first time in this group (and in every member 
of it) that the valency electrons do not all occupy the same type 
of orbit. In the typical and B elements there are two N x orbits 
and one N 2 : in the elements of the A subgroup two are in the 
electronic group of highest quantum number, and one is in the 
next group (for example, in scandium, 2 x 4 X and 1 x 3 3 ), and 
this arrangement of the two outermost electronic groups persists 
throughout the whole of the rare earth metals. Of this difference 
in the orbits of the valency electrons there is little trace in the 
chemical behaviour of the typical and A elements, but in the B 
subgroup there are signs of the two N n electrons refusing to act 
as valency electrons (the ' inert pair '), in univalent indium and 

The typical elements resemble the A subgroup in having the 
three valency electrons ' backed ' by an electronic group of 8, 
and the B subgroup in having all three in the same quantum 
group ; they thus have resemblances to both subgroups,' but do 
not quite belong to either. They also have peculiarities of their 
own, since with the increased valency the tendency to covalency 
formation predominates exclusively in boron, and considerably 
in aluminium. The B subgroup differs from the A in being less 
electropositive, as we should expect from the somewhat smaller 
atomic volume ; the metals also have lower melting-points, and 
the halides are more volatile. 

Typical Elements : Boron, Aluminium 

Boron is the only element with less than four valency electrons 
which cannot form a simple cation (owing to its small size) ; it 
is also the only element more than four places before an inert gas 
which gives volatile hydrides, these being of a peculiar type, 1 
such as B 2 H fl , in which the boron is apparently quadrivalent : 
they can only be explained by supposing that some of the 
hydrogen atoms are attached by 1 -electron links. Otherwise 
boron behaves as a normal tnvalent element, which readily 
completes its octet by co-ordination. Its halides, including the 
fluoride, are volatile and non-associated (for a possible reason 

1 See p. 108. 

306* M m 

266 Group III 

see p. 245) ; they are non-conductors. They are hydrolyzed by 
water to the very stable boric acid B(OH) 3 , which is remarkable 
for its extreme weakness (its first dissociation constant is 
l-7xlO~ 9 , about the same as that of hydrocyanic acid, and 
only about one-fifth of that of hydrogen sulphide), and for the 
great rapidity (only equalled by that of nitrous acid) with 
which its esters and acyl derivatives are formed and hydrolyzed. 
Of the numerous co-ordinated and chelate compounds of boron, 
many have already been mentioned (pp. 155, 222). 

Aluminium, having a larger atom than boron, can form a 
trivalent cation Al +++ , but it readily assumes the covalent state, 
and as readily increases its covalency from 8 to 4, and less 
readily to 6, by co-ordination. The ion, owing to its triple charge, 
easily takes up 6 molecules of water, and also quite frequently 
12, presumably in the form of double molecules (p. 199). The 
hydroxide A1(OH) 3 is amphoteric in character, forming alumin- 
ates ; it is in fact almost as much an acid as boric acid, and the 
so-called aluminium alkylates, which are volatile (e.g. A1(OC 2 H 6 ) 3 , 
M. Pt. 130, B . Pt . 205 under 14 mm.) are esters like the boric esters. 
The hahdes, except the fluoride, though they ionize in water, are 
clearly themselves covalent compounds, being very bad con- 
ductors ; their boiling-points are raised by their polymerization, 
which is shown in the vapour and in non-dissociating solvents. 
They form addition compounds with great ease with almost 
every class of organic compound, usually of the 1 : 1 type, as in 
R 2 C=O-*-AlCl 3 . The reactivity which the organic component 
often exhibits in these compounds is the basis of the Friedel- 
Crafts reaction. 

Subgroup HI A : Scandium, Yttrium, and the Rare Earth 


All these are transition elements in the wider sense of the term, 
since the neutral ' normal ' atom contains an imperfect inner 
group (2, 2, 4, 1) ; as such they are included in the frames in 
Bohr's table (p. 89). But chemically they have little of the 
properties of transition elements. The last electron in the 
penultimate group is almost as loosely held as the two in the 
outermost group, and acts entirely as a valency electron. They 
therefore behave, so far as the two outer electronic groups are 
concerned, as trivalent elements with a complete core in the 
scandium ion Sc +++ (2)(8)(8) and in the lanthanum ion La +++ 
(2) (8) (18) (18) (8) ; thus they are colourless and diamagnetic, 

Group III, Subgroup A 267 

with the exception of the elements from cerium (58) to ytter- 
bium (70), which are transitional for a different reason, owing 
to the imperfection of the antepenultimate (fourth quantum) 
group. These last all have the structure (2) (8) (18) (18 +X) 
(2, 2, 4, 1), in which X varies from 1 in cerium to 13 in ytter- 
bium. This imperfect group gives them their peculiar optical 
and paramagnetic properties (pp. 48, 214), but it is too far within 
the atom to affect the chemical properties seriously, except in 
the first two elements, cerium and praseodymium. All the rest 
have the group valency of 8 ; but cerium forms a definite series 
of quadrivalent eerie compounds, such as an oxide CeO a and a 
nitrate [Ce](NO s ) 4 , which are easily reduced to the cerous state, 
but are fairly stable. Corresponding quadrivalent praseody- 
mium compounds are known, but they are much less stable, and 
immediately oxidize cerous compounds to eerie. The later 
members of the series show no sign of becoming quadrivalent. 
This is because a new type of orbit is always less stable in the 
first elements in which it appears than in the later ones. When 
(in Ce 58) the nuclear charge is just large enough to draw an 
electron into a 4 4 orbit, this is not much more difficult to remove 
than the three valency electrons in 5 3 and 6 1 orbits ; but as the 
nuclear charge increases, the removal becomes less easy : it is 
just possible with praseodymium (59), but not with the succeed- 
ing elements. 

Of the properties of this subgroup in general, apart from the 
peculiarities of the rare earth metals, there is not much to be 
said. The elements are more electropositive than those of sub- 
group B, as would be expected from their larger atomic volumes ; 
the hydroxides are less acidic, and do not dissolve in alkalis like 
those of the B elements ; the halides are less volatile, and the 
metals form stable carbonates, which those of subgroup B do not. 

Subgroup III B : Gallium, Indium, Thallium 

The elements of this subgroup, in addition to being less 
electropositive than those of A, are remarkable for showing 
valencies lower than three. Gallium can be divalent, indium 
di- and univalent, and thallium umvalent : that is, one of the 
three valency electrons m gallium, one and two m indium, and 
two in thallium can become inactive. The inactivity of two 
electrons may fairly be taken to be an example of the indepen- 
dence of the N n group of outer electrons, for which the Stoner 
theory gives a reason (see p. 35) : there are many examples of 

268 Group IV 

this in the later periodic groups. The presence of a single inactive 
electron in divalent gallium and indium is difficult to explain. 
The compounds in which these lower valencies are exhibited, 
except those of univalent thallium, are all very unstable, and 
they are almost confined to the halides. Gallons chloride GaCl a 
decomposes water with liberation of hydrogen, while indium 
dichloride InCl 2 and monochloride InCl are converted in water 
(like cuprous salts) into the trichloride and metallic indium. All 
these three chlorides give a vapour of the normal density ; they 
are fairly good conductors in the fused state, which indicates 
the existence of the corresponding ions Ga ++ , In ++ , and In + . 

The thallous compounds (no compounds of divalent thallium 
are known) are much more stable, and show little tendency to 
-go over into the thallic state. The ion has been shown to be 
partly but not wholly polymerized in solution to [T1 2 ] ++ (pre- 
sumably + T1=T1 + ), and almost the only known thallous com- 
pounds apart from the salts appear to be the curious liquid 
alkylates Tl-O-Alk and the acetylacetonate T1A : no complex 
compounds of univalent thallium are described. In all these 
respects the thallous compounds resemble the mercurous. 

It is remarkable that thallium forms no mono- and no trialkyl 
derivatives, but only the salts of dialkyl thallium, such as 
[(CH 3 ) 2 T1]I, a very stable compound derived from a strong base 
[(CH 3 ) 2 T1]OH. 


Elements and atomic volumes : 

Ti 22 Zr 40 (Ce 58, Pr 59) Hf 72 Th 90 
C6 Si 14 18-7 21-8 200 21-8 (ca.23) 20-8 
7-6 11-4 

7-8 Ge 32 Sn 50 Pb 82 

18-2 16-5 18-2. 

Characteristic groupings : 

A : (C) (8, 2) 2. B : (C) (18) 2, 2. 

The tendency for ions with a charge as great as four units to 
pass into the covalent state can only be overcome when they are 
unusually large, and hence we do not find quadrivalent ions of 
any stability among the elements of this group until we reach the 
second long period (tin, and perhaps zirconium) ; the quadri- 
valent compounds of the earlier elements are all covalent. 

The main peculiarity of this group is due to the fact that since 

Group IV 269 

there are four valency electrons, the atoms can, by the direct 
production of four normal covalencies, acquire the exceptional 
stability given by the fully shared octet ; they therefore tend 
to rest content with this state, and not to increase their covalency 
by co-ordination ; this is especially true of the lighter elements, 
and the B subgroup generally. In the first member, carbon, this 
group covalency is at the same time the maximum covalency, 
and as a result compounds of quadrivalent carbon are peculiarly 
stable, since the atom has the stability of the fully shared octet, 
and further is unable to act either as donor or as acceptor. This 
is one main reason for the unique position of carbon. 

The characteristic difference between the subgroups which was 
observed in the previous groups that A was more electro- 
positive than B, and had less tendency to form covalencies 
grows weaker in each successive group, and in the fourth has 
practically disappeared, as has also the difference in atomic 
volume. Indeed the atomic volumes of the B elements are now 
somewhat the larger, owing probably to the difference in crystal 
structure : carbon, silicon, germanium and tin crystallize in the 
diamond form, while all the A elements have a close-packed struc- 
ture. 1 The two subgroups are sufficiently unlike in certain points, 
but it is a new kind of unlikeness ; it is mainly due to the 
transitional character of the A elements (which is further 
discussed below) and to the greater preference of the B elements 
for the 4-covalent state. This preference, which is not understood, 
is shown in the difference of crystal structure mentioned above, 
and still more clearly in the much smaller volatility of the halides 
of the A elements, with the exception of titanium. The most 
striking difference is that the typical and all the B elements form 
volatile hydrides and volatile alkyl derivatives, while none of the 
A elements do so ; this difference is found in all the subsequent 
groups. In all the points which distinguish the subgroups, the 
typical elements resemble the B subgroup and not the A. 

The most important of these distinctions depend on the changes 
of valency. Practically all the elements of the group are capable 
of a lower valency than four, but this is due to different causes, 
and exhibited in a different way, in the two subgroups. In the 
A subgroup we find the characteristic behaviour of transition 
elements, due to the possibility of some of the outer electrons 
(two in this group) acting either as valency electrons or as a part 
of the core : this leads to the lower valencies of three and two. 

1 See p. 107. 

270 Group IV 

In the B subgroup (and in the typical elements) no such electro- 
nic rearrangement is possible, and we might have anticipated 
that the valency would be invariably four ; but the two valency 
electrons of the N n grouplet show in these elements a peculiarly 
strong tendency to become ' inert ' and act as part of the core. 
These two effects can lead ultimately to the divalency of the 
elements of both subgroups, but the results differ in two ways. 
The transitional A elements are more stable in the trivalent 
state than in the divalent, whereas in theB elements the trivalent 
state does not occur at all except as a ' forced valency ' in very 
unstable compounds such as the tnaryl-methyls. Further, in the 
A subgroup the stability of the lower valencies diminishes as the 
atomic number increases (as happens in every group), whereas 
in the typical and B elements the opposite change occurs ; the 
inertness of the N u pair is always more marked in the later 
members of a subgroup. 

It will be convenient to consider first the typical and B elements 
and then the A subgroup. The following table, giving the boiling- 
points and conductivities of the tetrachlorides, and the action 
of water upon them, may be useful. 

Tetra- Eoilvng- Conduc- 

chlonde of point. timty. Result of Action of Water. 

Carbon 76 No action 

Silicon 57 Complete hydrolysis 

Germanium 86 Incomplete (reversible) hydrolysis 

Tin 114 lomzation (with some hydrolysis) 

Lead (ca. 150) 8xlO~ 7 (0 ) Pb++ + 2 Cl~ + C1 2 (and PbO 2 ). 

Titanium 136 TiCl 3 OH, TiCl 2 (OH) 2 TiCl(OH) 3 , 

Ti(OH) 4 

Zirconium red heat ZrOCl 2 
(Cerium : non-existent) 

Hafnium red heat HfOCl 2 

Thorium ca. 1,000 0-61(814) lomzation 

Group IV : Typical Elements and Subgroup B : Carbon, Silicon, 

Germanium, Tin, Lead 

Carbon is unique among the elements in the enormous variety 
of relatively stable compounds which it can form. Although 
silicon resembles it to some extent, we can now see that the 
organic chemistry of silicon, even if it were as fully worked out 
as that of carbon, would be found to be far less extensive. There 
are two main reasons for the exceptional position of carbon. The 
first is that in the 4-covalent compounds which it can form 
without co-ordination it not only has the great stability conferred 

Carbon 271 

by the fully shared octet, but also is covalently saturated : the 
octet cannot expand. The atom is therefore unable to co-ordinate 
either as donor or as acceptor, and so is much less open to chemi- 
cal attack, as we saw in comparing the action of water on the 
tetrachlorides of carbon and silicon (p. 157), or on chains of 
carbon and of silicon atoms (p. 159). This is the chief cause of 
the peculiar 4 sluggishness ' (Tragheit) of carbon, a disinclination 
to react which gives comparative stability to a large number of 
thermodynamically unstable compounds. The second reason is 
that the affinities of carbon for a variety of other elements are 
much more evenly balanced than is usually the case : carbon 
has no very strong preferences, and hence can form compounds 
of the most diverse types which yet are reasonably stable. The 
link between one carbon atom and another is remarkably strong, 
and is little weakened by repetition, so that the element can form 
stable chains of enormous length. Further, it has almost as 
great an affinity for hydrogen as for oxygen. It is a general rule 
that the first member of a group has the strongest affinity for 
hydrogen and usually the weakest for oxygen (compare nitrogen 
and phosphorus, or fluorine and chlorine), and in carbon (alone 
of the fourth group elements) the two are so near that its link 
with hydrogen is not usually broken by such weak oxidizing 
agents as atmospheric air. 

An important result of this exceptional stability of the normal 
4-covalent state of carbon is that (except in the divalent deriva- 
tives, which are discussed later) it shows the greatest reluctance 
to abandon it. Trivalency, as in the triaryl-methyls, where the 
atom has a valency group of 7, only arises under extreme com- 
pulsion, and is excessively unstable. lonization and co-ordination 
are unknown with carbon except as a means of escape from this 
tnvalent state. If a tnvalent derivative such as triphenyl-methyl 
is dissolved in a donor solvent like sulphur dioxide or ether, the 
latter forms a co-ordinate link with onetrivalent atom, thereby in- 
creasing its valency group from 7 to 9 : one of these nine electrons 
is taken up by a second trivalent carbon atom, and two ions are 
formed, in each of which the carbon has regained a complete octet : 


2 R ; c + : o i : Et 

R Et 

- R 

R : c : o : Et 

L R Et J 



+ IR;C 

_ R_ 

or more simply 

2 R 3 C + OEt 2 = [R 3 C^OEt] + + [R 8 C] 

272 Group IV 

The process is exactly similar to the conversion of an ammonia 
molecule into an ammonium ion and a free electron by addition 
of an atom of hydrogen : except that the nitrogen starts with a 
complete octet and the hydrogen adds one electron, while the 
carbon starts with a septet, and gains two electrons from the 
co-ordinate link ; in both cases since the valency group of 9 
which would be formed is unstable, one electron is lost. 

Among the general changes which occur in the series of ele- 
ments from carbon to lead, the most obvious is the fall in the 
affinity for hydrogen, from the very stable hydrocarbons to the 
hydride of tin, which decomposes on standing, and that of lead, 
which is apparently even more unstable. Even with silicon the 
difference is considerable : its most stable hydride SiH 4 de- 
composes rapidly at 300-400, and all the hydrides of silicon are 
decomposed by air, most of them being spontaneously inflamm- 
able. Silicon has a weaker affinity than carbon for hydrogen, for 
carbon, for itself, 1 and for nitrogen, but a stronger affinity for 
the halogens, and a much stronger for oxygen. 

In their quadrivalent compounds the elements show the nor- 
mal increase of metallic character with atomic number. This is 
indicated in the effect of water on the tetrahahdes, and may be 
said to culminate in tin, where we get the stable stannic ion. The 
position of lead is different : its metallic character is indeed well 
marked, but it is manifested only in the lower valency : the 
compounds of quadrivalent lead are all covalent. 

Every member of the series is known to form divalent com- 
pounds except silicon. It must however be remembered that 
though the compounds of divalent carbon are well known (as in 
carbon monoxide, the isocyanides and the fulminic derivatives, 
and the new diethoxymethylene C(OC 2 H 6 ) 2 ), they are very few 
in comparison with the quadrivalent compounds, and it is quite 
possible that if the same amount of attention had been given to 
silicon it also would have been found to be capable of becoming 
divalent. At any rate, apart from carbon the stability of the 
divalent form increases with the atomic number. Divalent 
compounds are unknown with silicon, very unstable with 
germanium, fairly stable (though less so than the quadrivalent) 
with tin, and the only electrovalent form with lead. This 
increase in the inertness of the N n pair is found in the later 

1 For a discussion of the mechanism by which the link of silicon to 
silicon is broken see p. 159. 

Group IV, Subgroup A 273 

periodic groups also. For some reason not yet understood, the 
inertness is peculiarly strongly marked in one vertical and in one 
horizontal series in the periodic table : in the series we are now 
considering, the typical and B elements of the fourth group, and 
in the successive elements following gold : mercury, thallium, 
lead, and bismuth (see p. 179). In lead, which is common to both 
of these series, it takes the peculiar form that the N 1X grouplet (or 
at any rate two of the four valency electrons) is available for 
sharing but not for ionization : the only ions of lead are the 
plumbous Pb ++ , while in the covalent compounds all four elec- 
trons are active. This is the cause of the remarkable reaction of 
lead chloride with zinc alkyls, in which metallic lead separates : 
2PbCl a + 2Zn(CH 3 ) 2 = 2 ZnCl 2 + Pb(CH 3 ) 4 + Pb. 
It is of course on this change of valency that the action of the 
lead accumulator depends. 

Subgroup IV A : Titanium, Zirconium (Cerium, Praseodymium), 
Hafnium, Thorium 

This is the first group in which the A elements show the true 
transitional characteristics, with a variation of the valency by 
single units through the inclusion of one or more (in this group 
one or two) valency electrons in the core. 

In the compounds with the group valency of four, there is the 
normal increase with atomic number of the metallic character, 
that is, of the tendency to ionization, culminating in thorium, 
whose tetrachloride shows no signs of covalency. In zirconium 
and hafnium, where the atom is presumably not large enough for 
ionization with a quadruple charge, a compromise is effected 
through the formation of the divalent ' yl ' ion [X=O] ++ (Zr=0, 
Hf =O), in which the metal, having only a double charge, can 
resist the tendency to form further co valencies. This kind of 
complex ion is not uncommonly formed by the A elements of 
the later groups. We do not know why the tetrahalides of 
zirconium and hafnium are so much less volatile than those of 
the B elements, nor why this difference does not extend to 
titanium. It is however clear that for some reason the A 
elements are less stable in the 4-covalent state than the B, and 
it is possible that this causes the halides to polymerize. 

Cerium and praseodymium must be regarded as belonging to 
this subgroup in their quadrivalent state, though in the trivalent 
they belong to III A. When we examine the elements of Sub- 
Sofa N n 

274 Group IV 

group IV A in detail, it becomes obvious, both from the chemical 
point of view and from that of atomic structure, that they can- 
not be treated as a linear series Ti-Zr-Ce (Pr)-Hf-Th. The 
normal relation between the successive elements of a subgroup 
is that each has a whole quantum group in its core more than the 
one before it, and thus has its valency electrons in the next 
higher quantum group. This is the relation between titanium 
and zirconium, and between hafnium and thorium. But cerium 
and hafnium both have their valency electrons in the fifth and 
sixth quantum groups, and differ only in that the fourth (ante- 
penultimate) quantum group contains 18 electrons in cerium and 
82 in hafnium (with a corresponding increase of 14 units in the 
nuclear charge) : 

22 Ti : (2)(8)(10)2 
40 Zr : (2)(8)(18)(10)2 
58 Ce : (2)(8)(18)(18)(10)2 
72 Hf : (2)(8)(18)(82)(10)2 
90 Th : (2)(8)(18)(32)(18)(10)2 

(Cerium is here given not in the true ' normal ' form, but in the 
less stable form from which its quadrivalent compounds may be 
supposed to be derived.) 

It thus appears that cerium and hafnium should be regarded 
not as successive links in a linear series, but as two alternative 
links between zirconium and thorium, the chain of elements being 
branched at this point : 

Ti - Z Th. 

Accordingly we find that the properties of quadrivalent cerium 
are not intermediate between those of zirconium and hafnium, 
but are in every way nearer to those of thorium. The properties 
of zirconium and hafnium are almost identical. The tetra- 
hydroxides of zirconium and hafnium are weakly acidic, while 
those of cerium and thorium are not : the peculiar metastabihty 
of the forms of thorium sulphate is repeated with the eerie salt, 
but not with that of hafnium : the tendency to form double 
nitrates is common to thorium and cerium, but is not shared by 
hafnium. It is probable that the unparalleled resemblance be- 
tween zirconium and hafnium, which is greater than that be- 
tween any other two elements outside the rare earth series, and 
probably as great as that between any two of the rare earth 

Group IV, Subgroup A 275 

metals themselves, is at least partly due to this peculiar relation 
in structure, and that the increase of the fourth quantum group 
from 18 to 82, together with the increase in the nuclear charge, 
in some way neutralizes the effect of increasing by one the princi- 
pal quantum number of the valency electrons. The resemblance 
recurs, though to a diminishing extent, in the pairs niobium and 
tantalum, and molybdenum and tungsten, which have similar 
structural relations. 

The greater stability of the highest covalencies in subgroup 
IV A as compared with IV B is shown by the extreme rarity of 
a covalency of 8 in the B subgroup. In A, as soon as a covalency 
of 8 becomes possible, a whole series of 8-covalent compounds 
with /?-diketones, &c., of the type MA 4 are formed ; they have 
been prepared with zirconium, cerium, hafnium, and thorium (see 
pp. 156, 169). No compounds of this type are known in subgroup 
B. Tin, which has been examined in great detail, forms some 
compounds in which it is 8-covalent, but they are all of more 
complicated types, and the same is true of lead. The difference 
in atomic volume (Zr 21-8, Ce 20 0, Th 20-8 : Sn 16 5, Pb 18-2), 
although it is in the right direction, does not seem large enough 
to account for this. 

In the compounds in which these elements show a valency less 
than four, we find a tendency common to all transition elements, 
that in each group the stability of the lower valencies diminishes 
as the atomic number increases. Titanium is definitely trivalent 
(although the compounds readily pass into the quadrivalent 
state), and must be divalent in the dichloride and dnodide, 
although their molecular weights are unknown. Zirconium was 
until lately supposed always to be quadrivalent : trivalent and 
even divalent zirconium compounds have recently been prepared 
(as a trichloride and a dichloride), but they are less stable than 
those of titanium ; while thorium shows no signs of a valency less 
than four. The trivalency of cerium and praseodymium is of 
course due to a different cause, and does not concern us here. 



Elements and atomic volumes : * 

V23 Nb41 Ta73 Pa 91 A. 

9-3 13-3 16-8 

N7 P15 As 33 Sb51 Bi 83 B. 

(15-7 18-3 13-2 18-7 21-4 

atB. Pt.) 16-9 16-0 23-0 

A : (C)(ll)2 or (C)(12)l. B : (C)(18)2,3. 

The general relations are characteristic of all the later groups. 
The typical elements belong clearly to B and not to A ; A 
resembles B only in those compounds in which the atoms have 
the group valency. In their lower valencies the elements of 
subgroup A should not be compared with the other elements of 
this group, but with the A elements of groups IV and VI. It 
is therefore better to treat the two divisions of the group 

Typical Elements and Subgroup B 

This is the first group in which we meet with mixed octets. 
The ordinary valency of the atoms is three (as m NH 3 ), the five 
valency electrons being increased to eight by the formation of 
three normal covalencies, giving the valency group 2, 3, 3. (The 
formation of simple cations with an electrovalency of five in 
anything but the minutest quantities is of course impossible.) 
The covalency can be increased to four, with the production of a 
fully shared octet, either by co-ordination as in (CH 3 ) 3 N-^0, or 
by loss of an electron as in [NHJ" 1 ". By the expansion of the 
octet, except in nitrogen where this is forbidden by the covalency 
rule, 2 a covalency of five can be reached, as in PF 6 , and this can 
be increased to higher values by co-ordination. A covalency of 
five (like all odd covalencies) is as a rule comparatively unstable, 
but it is more stable with element^of group V than elsewhere, 
since they can form it by the normal sharing of the five valency 
electrons (with five others from the attached groups) without the 
electrostatic disturbance caused by co-ordination. Even in this 
group, however, it readily goes over into the octet form wherever 

1 Where two values are given for one element they refer to allotropic 

a For the evidence that nitrogen cannot have a covalency of more than 
four, see p. 158. 

Typical and B Elements 277 

the nature of the attached atoms permits. It is almost confined 
to the pentahalides : in those oxygen compounds m which the 
atom is ordinarily written with a double link to oxygen, we have 
evidence (confirmed by the observation of the parachor 1 ) that 
the link is really co-ordinate, and the atom 4-covalent, as in 

CK C 2 H 3 0\ 

C1-^P->O and C 2 H G O- 
CK C 2 H 6 0/ 

The elements of this series are remarkable for occurring in 
two well-marked allotropic forms, a less dense transparent form, 
usually low-melting and more soluble in non-associated organic 
solvents, and a more dense, opaque, and more or less metallic 
form. The latter becomes increasingly stable as the atomic 
number rises ; it is non-existent in nitrogen, and is the only form 
in bismuth. The transparent form is always metastable except 
in nitrogen ; but it is least so in phosphorus and most in anti- 
mony. The metallic character and the tendency to iomzation 
increase down the series, as is shown, for example, in the behaviour 
of the halides with water. That of nitrogen is peculiar ; as we 
have seen, the nitrogen, since it cannot increase its octet, must 
act as a donor in co-ordinating with the water, and so attach 
itself to the hydrogen of the latter. This causes hydrolysis to 
hypochlorous acid and ammonia : 
Cl Cl\ 

-* CHN->H-O-H -+ NH S + H-O-CI. 
ci/ ci/ 

With the other elements the octet can expand, and so the water 
can co-ordinate through the oxygen, which it is always more 
ready to do : 


CAP -> CAP-O< -> P(OH) 3 + HC1. 


This leads to hydrolysis to hydrochloric acid and the hydroxide, 
unless the central atom can exist as an ion. With phosphorus 
the hydrolysis is complete, with arsenic less so ; with antimony 
the main product is the univalent ion [Sb =0] + , with some 
Sb +++ ion ; with bismuth similar changes occur, but the Bi +++ 
ion is much more stable. 

The affinity for hydrogen falls off in the normal manner, from 
the very stable ammonia to bismuth hydride, which decomposes 

1 See p. 127. 

278 Group V 

at the ordinary temperature with a half life period of some 20 
minutes. The basicity of these hydrides falls off in the same way, 
phosphine being a very weak base, and the other hydrides scarcely 
basic at all. This is no doubt a direct result of the diminishing 
affinity for hydrogen, since the basicity depends on the formation 
of a fourth hydrogen link in [XH 4 ] + . 

The stability of the true 5-covalent compounds such as the 
pentahalides also diminishes with rise of atomic number, but 
apparently with some irregularity. Phosphorus forms pentaha- 
lides with fluorine, chlorine, and bromine (the stability diminishes 
as the atomic weight of the halogen increases) arsenic only with 
fluorine, antimony with fluorine and chlorine and in complexes 
with bromine, while bismuth forms none at all. But mixed 
alkyl or aryl halides such as (CH 3 ) 3 AsCl 2 are formed by all four 
elements ; compounds of this type (with aryl, not with alkyl 
groups) afford the only known examples of 5-covalent bismuth, 
and these are very unstable. 

There is a certain ambiguity about the structure of the triva- 
lent atoms of elements of this group. On the analogy of the 
neighbouring groups we should expect to find a tendency in the 
heavier elements for two of the valency electrons to become 
inert and behave as part of the core. This would reduce the 
valency to three, and make the atoms resemble those of the third 
group elements, in which there are only three valency electrons. 
On the other hand the same valency of three can arise through the 
formation of a mixed octet 2, 3, 3. In nitrogen and the earlier 
members generally there is no reason to suppose that the 
trivalency has any other cause than mixed octet formation. 
But with the later members, and especially bismuth, there is 
evidence that the inertness of the N 1]L pair is operative, and that 
the atoms are in a state resembling that of a third group element 
such as yttrium or lanthanum. This evidence is of various kinds ; 
there is the metallic nature of the element itself, and the exis- 
tence ot simple ions such as Bi +++ , which has the structure (60) 
(18) (2), which could hardly be stable unless the last two electrons 
were inert. So too the stable ' yl ' ions [Sb=O] + and [Bi=0]" t " 
have the E.A.N. (C)(18)(2,2,2), with a mixed sextet scarcely 
known elsewhere except in such atoms as that of divalent 
carbon, where it is explained by the strong tendency of the N n 
grouplet to be inert in the elements of the fourth periodic group. 
There is further the tendency, which is increasingly strong in 
the heavier members of the subgroup, to form complexes derived 

Typical and B Elements 279 

from the simple trivalent compounds, such as K[BiCl 4 ], 
[BiBr 35 2NH 3 ], and K 3 [Bi(CNS) fl ]. The effective valencies 
(see p. 164) of the bismuth atoms in these compounds are 
5 4 , 7 5 , and 9 G respectively, so that their valency groups are 
10 4 , 12 5 , and 14 6 , or (2,4,4,) (2,5,5), and (2,6,6). The occurrence 
of mixed valency groups of more than 8 electrons is practically 
if not absolutely confined to elements in which on other grounds 
we have reason to expect the N n pair to be inert. That in this 
subgroup E.A.Ns of this form are abundant among the com- 
pounds of bismuth, not uncommon among those of antimony, 
but with one or two doubtful exceptions absent from those of 
the lighter elements, is a further confirmation of this view, since 
the inert pair is always more marked in the heavier elements of a 
group. There are other points of resemblance between bismuth 
and the metals of the third group, especially the formation of a 
series of complex nitrates of the formula M" 3 [M"'(N0 3 ) 6 ] 2 , 
24H 2 O, in which M" is magnesium, zinc, cobalt, or nickel. 
M"' may be either bismuth or lanthanum, cerium, praseody- 
mium, neodymmm, samarium, or gadolinium. 

Nearly all the elements of this series form a certain number 
of ' anomalous ' compounds, in which they show valencies which 
cannot be explained in the present state of our knowledge. 
Nitrogen gives the familiar nitric oxide NO and nitrogen 
dioxide NO 2 , both of which are ' odd molecules ' and are 
paramagnetic. Analogous organic derivatives (C 6 H 5 ) 2 N and 
(C 6 H 5 ) 2 NO are known. Nitrogen dioxide from its tendency to 
polymerization may perhaps be compared with triphenyl methyl ; 

both, if we write the nitrogen compound N^ , have the same 

valency group, a septet (1, 3, 3) ; the di-aryl nitrogens Ar 2 N, 
which also polymerize readily, may be referred to the same type. 
Nitric oxide, if it is correctly written N=O, also has a septet 
(3 5 2, 2) ; but it shows a stability which it is difficult to reconcile 
with so unusual a structure. It is, of course, easy to write the 
molecule so that it has two complete octets, if we assume that 
the nitrogen shares three electrons belonging to the oxygen, and 
the oxygen two belonging to the nitrogen ; but this involves the 
assumption of a link of five shared electrons, which we have no 
other reason to suppose to be stable. 

Phosphorus gives an anomalous compound in hypophosphoric 
acid H 2 PO 3 . It is easy to formulate this if we are allowed to 
double its formula, but the evidence, both from the conductivity 

280 Group V 

of solutions of the salts, and from the molecular weight in solu- 
tion of its esters R 2 P0 3 , is in favour of the simple formula. If 
this is adopted, we cannot reconcile it with any recognized 
valency of phosphorus ; the acid may be written either 

H-CK H-0\ 

>P=O or >P->0, 


assigning to the phosphorus a valency group either of (1, 4, 4), 
or (1, 8, 3). In the same way certain complex salts of antimony 
have been described which arC derived from a tetrahalide 
SbX 4 , such as Rb 2 [SbCl 6 ] and (NH 4 ) 2 [SbBr 6 ]. 

At present we can do no more than note the existence of such 
anomalous compounds. 

Subgroup V A: Vanadium, Niobium, Tantalum, Protoactinium 
Melting-points of elements, and boiling-points of pentahalides : 

V Nb Ta Pa 

M. Pt. of 

Element 1780 1950 2800 


ofXF 6 111 220 229 

ofXCl B 241 242 

These elements show the characteristic valency relations of 
an A (transitional) subgroup. They have amongst them all 
possible valencies from 2 up to the group valency of 5, and it is 
only in this last state that they show any resemblance to the 
elements of the B subgroup. The metallic characteristics are 
confined to the lower states of valency, since the smaller charge 
renders iomzation possible, and it is particularly to be noticed 
that in their trivalent compounds they have no resemblance to 
trivalent nitrogen or phosphorus. This maybe taken as evidence 
that trivalent vanadium, for example, in its covalent compounds 
has not a mixed octet (2, 8, 8), as nitrogen and phosphorus have 
in NH 3 or PC1 3 , but a sextet (8, 8), the other two potential 
valency electrons forming part of the core : (2) (8) (10) 8,8. 

In their quinquevalent compounds there is a general similarity 
between these elements and those of subgroup B. It is curious 
that just as arsenic shows less tendency to form pentahalides 
than either phosphorus or antimony, so vanadium, in the same 

Subgroup A 281 

long period as arsenic, refuses to form a pentachloride like 
niobium and tantalum, although a pentafluoride has recently 
been discovered. The analogy between the two subgroups is 
chiefly shown in the derivatives of the ions XO 4 . Vanadic acid, 
apart from its oxidizing power, which depends on the transitional 
character of the element, resembles phosphoric in many of its 
properties, as we should expect, but differs conspicuously from 
it in two ways. The various forms of phosphoric acid and their 
ions (ortho, meta, pyro) are relatively stable, and only change 
slowly into one another in solution. But with vanadic acid the 
corresponding changes are very rapid : the solution of a vana- 
date contains all the forms of ion in equilibrium, and can be made 
to precipitate a salt of any one of them by a suitable modifica- 
tion of the conditions. A similar ease of transformation is found 
among the esters, which is an almost unparalleled phenomenon. 
Secondly, whereas the ultimate effect of hydrolysis or acidifica- 
tion on a meta- pyro- ororthophosphateistogiveorthophosphoric 
acid H 3 PO 4 or its ions the simple form with one phosphorus 
atom in the molecule the opposite effect is produced on a 
vanadate. The simple form of ion VO 4 '" is only stable in pre- 
sence of excess of hydroxyl ion, and is converted by hydrolysis 
or acidification through the increasingly complex forms of pyro- 
V 2 7 "", meta- V 3 O 9 '" and hexavanadate V 6 O 17 "", finally into 
the highly polymerized vanadium pentoxide (V 2 O 5 ) n , which is 
scarcely soluble in water, and forms no crystalline hydrates. 
This may be compared with the behaviour of a chromate, which 
gives on acidification the polymerized bichromate ion Cr 2 O 7 ". 

In comparing the members of the subgroup with one another, 
we find, as in subgroup IV A, that there is a marked difference 
between the first member (first long period) and the second and 
third, which resemble one another closely, though not so closely 
as zirconium and hafnium. Of the last member, protoactinium, 
little is known beyond the fact that it resembles its predecessor 
tantalum. The relations are best illustrated by comparing the 
properties of niobium and tantalum with those of vanadium. 

Niobium and tantalum always occur together in nature, and 
it was long before any satisfactory method of separation was 
discovered. The first point of difference from vanadium is in the 
stability of the lower valencies. Vanadium forms quite definite 
series of di-, tn-, and quadrivalent compounds. It was formerly 
thought that niobium could be quadri- and tri- but not divalent, 
and tantalum quadri- but neither tri- nor divalent. Recent work 

3 o6 

282 Group V 

has however shown that the relations are not quite so simple. 
Niobium can certainly be quadri- and trivalent. With tantalum 
the facts are less clear, but it is certainly sometimes trivalent, 
and probably quadrivalent ; and it is remarkable that there is 
definite evidence of divalent tantalum, though none of divalent 
niobium. 1 It still however remains true that in subgroup V A as 
in IV A the lower valencies are more stable in the first member 
than in the two following. 

The quinquevalent oxy-acids (vanadates, niobates, and tanta- 
lates) have a common tendency to form condensed or polymer- 
ized ions, but vanadic acid is much stronger than the other two : 
the alkaline niobates and tantalates are decomposed by carbon 
dioxide with precipitation of the pentoxide. This is even more 
marked in the complex acids ; those of vanadium are much 
stronger than the original acid, while those of niobium and 
tantalum are not. In this respect the niobates and tantalates 
resemble the titanates, zirconates, and stannates more than the 
vanadates. This is an example of the increasing basicity of the 
heavier members which is common to all A and B subgroups : 
in the same way the phosphates are more acidic than the 
arsenates, and these than the antimonates. 

Another difference which may be referred to the same genera 
tendency is the increasing affinity for halogens as compared Witt 
oxygen. Vanadium forms no pentachloride or pentabromide 
but it forms both VOC1 3 and V0 2 C1 : niobium forms NbCl 5 anc 
NbOCl 3 , but the evidence for Nb0 2 Cl is very weak : tantalun 
forms a pentachloride and a pentabromide, but no oxy-halidei 
at all. If the pentoxides of the three elements are dissolved ii 
hydrofluoric acid of the same concentration, and an alkalm< 
fluoride MF is added, the salts which separate most easily are 

with vanadium : V0 2 F, #MF, /H 2 O 
with niobium : NbOF 3 , oMF, ?/H 2 O 
with tantalum : TaF 5 , 0MF, ?/H 2 0. 

The fluoxytantalates, unlike their vanadium and niobmn 
analogues, can only be prepared in the absence of free hydro 
fluoric acid, which converts them into the fluotantalates. 

1 The spectroscopic evidence (p. 46) shows that the penultimat 
electronic group is more stable in the second transitional series of element 
(Zr-Pd) than in the Gist (Ti-Ni) or the third (Hf-Pt), and that whil 
vanadium and tantalum have in the ' normal ' state two electrons in th 
outermost quantum group, niobium only has one. 



Elements and atomic volumes : 

Cr24 Mo 42 W 74 U 92 A 

7-5 11-2 9-6 12-8 

08 S16 Se34 Te 52 Po 84 B 

14-3 15-6 16-5 20-6 

(atB.Pt.) 16-4 17-6 

A : (C)(12)2 or (C)(18)l. B : (C)(18)2,4. 

The elements of the A subgroup again have smaller atomic 
volumes than those of the B, and the difference is more marked 
than in group V ; it is no doubt due to the metallic structure and 
closer packing of the A elements. The resemblance of the A 
elements to the others becomes more restricted in each successive 
group, as the highest valencies become less important. 

Typical and B Elements 

This is the first group in which we find monatomic anions. 
On the Fa jans theory, ionization in this sense should take place 
more easily in the later members of the group, but the difference 
in size is not great. On the other hand the later elements, 
especially tellurium, can form quadrivalent cations : this is due 
to the inertness of the N 1:l pair, which reduces the available 
valency electrons to four, and makes the element behave like 
a fourth group metal such as tin, the Te ++++ ion, with a structure 
(2) (8) (18) (18) (2), having a stability approaching that of the 
stannic ion (2) (8) (18) (18). 

The covalent compounds are of more interest. The elements 
have a covalency of 2 in mixed octet formation (4, 2, 2), as 
in H 2 S, and by loss of an electron can form a tricovalent com- 
plex cation, as in the oxonium and sulphonium salts, such as 
[(CH 3 ) 2 O-H]X and [(CH 3 ) 3 S]X. There is less tendency to form 
oxonium or sulphonium than ammonium salts, presumably 
because the former lack the stability of the 4-covalent atom. 
A covalency of 3 and even of 4 maybe attained by co-ordination : 
oxygen, whether as hydroxyl or in the groups C O C or C=O, 
is very ready to form such a link. A second co-ordinate link 
(making a covalency of 4) is rare with oxygen, but occurs in such 
compounds as the basic beryllium acetate ; it is commoner 
with the heavier elements. With the exception of oxygen all 

284 Group VI 

these elements can form a valency group of 12 (tellurium of 
16), as in the hexafluondes, but most of them assume the octet 
form where possible, as in the sulphones and sulphuric esters 

R, R-<\ ..O 

>S-*0 and )S< 

R/ R-CK ^ 

This tendency to prefer the octet is however less marked than 
in group V, presumably because a covalency of 5 (decet), 
which with the latter element is the alternative to the octet, 
is less stable than a covalency of 6. There is evidence from the 
parachor (p. 129) that sulphur trioxide is at least partially in 
the 6-covalent form, and in telluric acid (see below) this is the 
stable form, and not the 4-covalent as in selenic and sulphuric 

The main differences between oxygen and sulphur are as 
follows : 

(1) Sulphur is more acidic than oxygen, as may be seen by 
comparing water (dissociation constant 2 x 1(T 16 ) with hydrogen 
sulphide (first dissociation constant 1(T 7 , second 10 ~ 16 ), or 
alcohols with mercaptans, or amides with thioamidcs. This is the 
opposite of what we should have expected on general grounds 
and on the Fajans theory : it may perhaps be due to the much 
smaller association of -S-H as compared with -0-H, dis- 
cussed below under (4). 

(2) The link between sulphur and sulphur is much stronger 
than that between oxygen and oxygen, and in consequence 
sulphur is much more ready to form long chains. The existence 
of S 8 molecules in the vapour and in solution, while oxygen is 
2 or in the metastable form 3 , is evidence of this . In compounds 
no examples of a chain of more than two oxygen atoms are 
known except the very unstable ozonides, and even compounds 
with two linked oxygen atoms, such as hydrogen peroxide and 
the organic peroxides and per-acids, decompose very readily. 
Chains of two, three, and even more sulphur atoms (as m the 
poly sulphides) are readily formed and are stable. These relations 
are the reverse of those observed in group IV, where the first 
element carbon forms far more stable and longer chains than the 
second silicon. 

(8) Sulphur has a much stronger tendency to assume a 
valency greater than two. It can of course exert a covalency 
of six, while oxygen is limited to four ; but even m the com- 
pounds in which sulphur retains its octet, it shows a much 

Typical and B Elements 285 

greater stability with covalencies of three and four than does 
oxygen. The comparison of the sulphonium and oxonium com- 
pounds illustrates this, and we have also such compounds as 
the sulphoxides, sulphones, and sulphates, to which oxygen offers 
no analogy. 

(4) A curious difference is that while the hydrogen of a hy- 
droxyl group readily acts as an acceptor, that of a sulphydryl 
group -S-H has no such power. " Hence hydrogen sulphide 
and the mercaptans are not associated, as may be seen by com- 
paring their boiling-points with those of then* oxygen analogues 
(those of ethyl ether and diethyl sulphide are added to show the 
normal effect of the greater atomic weight of sulphur) : 

Boiling-points Difference 

H-O-H 100 H-S-H -60 +160 

CH 3 -0-H 66 CH 3 -S-H +6 +60 

C 2 H 5 -0-H 78 C 2 H 5 -S-H +36 +42 

(C 2 H B -0-C 2 H 6 85 C 2 H 6 -S-C 2 H 6 92 -57) 

In the series sulphur selenium tellurium we find the usual 
fall in the affinity for hydrogen and increase in the metallic 
character as the atomic number rises. This last change is largely 
due to the increasing stability of the form in which the first two 
valency electrons behave as part of the core. This may be seen 
by considering the quadrivalent compounds. Some of these are 
really octet compounds with a co-ordinate link, like the sulph- 


oxides -n^S-j-O, and need not be further discussed ; but in such 

substances as the tetrahalides the valency group has increased by 
four, and so must have the form (2, 4, 4). Again in the quadri- 
valent ions such as Te ++++ the core contains two electrons more 
than the complete groups (48 electrons instead of 46). Such 
structures are scarcely possible unless these two unshared 
electrons are, in the sense in which we have used the word, 
inert. We should therefore expect them to be more prevalent 
in the heavier elements, and this is found to be so. The only 
definite sulphur compound of this type 1 is the tetrachlonde, 
which decomposes at 40 ; selenium forms a tetrafluoride 
(B. Ft. + 100), and a tetrachloride which is stable up to high 
temperatures. The tellurium compounds are still more stable ; 
they include such substances as the tetrachloride (M. Pt. 224, 
B. Pt. 414), the tetrabromide (M. Pt. 880, B. Pt. ca. 420), and the 
1 We may assume that sulphur dioxide has the structure O=S->O. 

286 Group VI 

dimethyl diiodide (CH 3 ) 2 TeI 2 , remarkable for existing in two 
isomeric forms, showing that the four attached groups lie in a 
plane (p. 281). The tetrachloride behaves m the fused state as 
if it were at least partially ionized ; at its melting-point it has 
the conductivity of a salt (0 115 at 236). Still more like salts 
are the quadrivalent compounds of the oxy-acids, such as 
Te(N0 3 ) 4 and Te(S0 4 ) 2 , which show the existence of the quadri- 
valent cation Te +++4 ~. 

There is a remarkable difference between telluric acid and its 
selenium and sulphur analogues . Sulphuric acid might have either 
of two formulae 

H-Ov -O H-Ov ,O 

(A) >S<: (B) >S/ . 

H-CK *0 H-(K X) 

It combines with water with great readiness : if it had the first 
formula we should expect its hydrates to be formed by coordina- 
tion, and to have such formulae as 

H-Ov -0->Hv H-Ov -0-^H-O-H 

X > r X 

- ^-/ -/ ^ 

If it had the second structure (B), the hydration should involve 
the conversion of the doubly linked oxygen into two hydroxyl 
groups, giving = S(OH) 4 and S(OH) 6 . In the latter case the 
compound should be able to act as a tetra- or hexabasic acid, but 
of this there is no indication. 1 We may therefore assume that sul- 
phuric acid has the first structure (A), and that its hydrates are 
formed by co-ordination. This conclusion has recently been con- 
firmed by the measurement of the parachors of the alkyl sulphates. 
Selenic acid behaves like sulphuric, and must have the correspond- 
ing structure. Telluric acid, on the other hand, is quite different. 
H 2 Te0 4 does not exist at all. The acid is precipitated from the 
aqueous solution of one of its salts in the form usually written 
H 2 Te0 4 , 2HO, that is as Te(OH) fl . This does not lose water below 
140, and when it does, it goes straight to the trioxide without 
any intermediate formation of H 2 Te0 4 . The formula Tc(OH) 6 
is further supported by the formation, on methylation with 
diazomethane, of an ester Te^-CEy,,. The ordinary tellurates 
all contam at least two molecules of water, which cannot be 
removed without deep-seated decomposition : these are ob- 

1 Unless the existence of compounds such as turpeth mineral 
HgSO 4 ,2HgO = Hg 3 S0 6 is to be taken as proof that this structure can 
occasionally be assumed. 

Subgroup A 287 

viously of the form K 2 H 4 Te0 6 . There are also tetrabasic salts 
such as Na 4 Te0 5 ,8H 2 0, which should be written Na 4 H 2 TeO 6 , 
7H 2 O, and hexabasic, as Ag 6 TeO 6 and Zn 3 TeO 6 . It is to be 
noticed that the next element to tellurium behaves in the same 
way : periodic acid is not HI0 4 but H 5 IO 6 . This change in 
behaviour is not likely to be due to the double link to the oxygen 
being more strained when it is attached to one of the heavier 
elements : it is more probable that the octet form becomes less 
stable as the covalency maximum increases. 

Subgroup VI A : Chromium, Molybdenum, Tungsten, Uranium 
Boiling-points of polyhalides : 

X = Cr Mo W U 

V XC1 5 268 276 

' XBr 5 338 

XF 85 19-5 56 

XC1 6 347 

In compounds in which they have the group valency of six 
these elements show the usual resemblance to those of the B 
subgroup. All except chromium form very volatile hexanuo- 
rides, and all form stable acids of, or derived from, the type 
H 2 XO 4 . These acids show a steady fall in acidity with increasing 
atomic number, as we should expect : they also, like those of the 
elements of subgroup V A, have a tendency to condense, which 
*.; is noticeable even in the first of them (in the formation of bi- 
chromic acid), and is especially marked in molybdic and tungstic 
acids, where it leads to the formation of the enormous and 
complicated group of the heteropoly-acids and their salts, of 
/ which K 4 H 4 [Si(W 2 7 ) a ],16H 2 is an example. In their general 
properties there is a close resemblance between molybdenum and 
tungsten (as there is between niobium and tantalum, and still 
more between zirconium and hafnium), while these elements 
differ much more from chromium 011 the one hand and uranium 
on the other. 

The formation of polyhalides in this series is peculiar. All the 
members except chromium form very volatile hexafluondes, 
tungsten a hexachlonde (the only known compound XC1 6 ), and 
molybdenum and tungsten also give pentahahdes. Chromium 
forms neither penta- nor hexahalides ; in this it resembles 
vanadium and arsenic (which give no pentahalides except with 

fluorine), so that the instability of this form of molecule seems to 
be common to the elements of the first long period. 

The elements have every possible valency from two to six ; 
as the atomic number increases, the stability of the lower 
valencies diminishes, and where they occur, the compounds tend 
to be covalent and not ionized. Apart from the group valency ol' 
six, which they all exhibit, the most important valencies are : 
for chromium two in the unstable chromous and three in the 
stable chromic ion : for molybdenum a valency of two is con- 
fined to derivatives of Mo 3 Cl 6 , whose structure is still obscure, 
although it behaves in some ways as a salt [Mo 3 Cl 4 ]Cl 2 : valencies 
of three and five are definitely established, and four is probable : 
with tungsten two, three, and four are probable but certainly 
unstable, while five is well established ; with uranium, valencies 
of two and three are excessively unstable, while that of four 
occurs in a form unknown in the lighter elements, that ol' a 
simple ion U ++++ , which undoubtedly exists, although it is readily 
oxidized to the much more stable uranyl ion. A valency of live 
with uranium is uncertain, depending on such compounds as 
the pentachlonde, which is solid, and may be a compound of 
the tetrachloride and hexachloride. Uranium is peculiar in 
forming the very stable uranyl ion [0 = U=0"] f+ ; this may be 
compared with such ions as zirconyl [Zr = 0] + " H , and it is to be 
noticed that just as ions of the zirconyl type, with one doubly 
linked oxygen, are not formed by the lighter elements, HO the 
uranyl type, with two such oxygen atoms, only occurs with the 


Elements and atomic volumes : 

Mn25 Ma 43 Re 75 A 

7-4 _ 

F9 C117 Br35 158 (85) B 

16-7 22-2 25-1 25-6 

(B.Pt.) (B.Pt.) (0C.) 

A: (C)(18)2 or (0(14)1. B: (C)(18)2, 5. 

The resemblance between the subgroups, being limited to 
compounds in which the elements have a valency of seven is 
only found m the ions rX0 4 f and their derivatives 

Halogens 289 

Typical Elements and Subgroup B : Halogens 

The halogens, having one electron less than an inert gas, form 
as well marked a series as the alkali metals, which have one 
electron more ; but their behaviour is more diverse, because it is 
not confined, as that of the alkali metals practically is, to the 
properties of the simple ions, but includes the formation of 
covalencies, which varies along the series, being largely affected 
by the atomic number. The one electron needed to make up 
the inert gas number is readily acquired either by transference 
or by sharing : the halogens form stable univalent compounds, 
both ionized and covalent, the former distinguished from the 
latter by their low volatility and high conductivity in the fused 
state and in ionizing solvents. The relative stability of these two 
forms depends both on the positive and on the negative consti- 
tuent. The influence of the former is indicated by Biltz's measure- 
ments of the electrical conductivity of the fused chlorides 
(p. 105). Briefly, he found that nearly all the chlorides had a 
conductivity at the melting-point either greater than 0-1 (ohm" 1 
cm." 1 ) or less than 10~. Among the typical and A elements 
good conductors are formed by all those of the first group except 
hydrogen, all of the second except beryllium, all of the third 
except boron and aluminium, and none of the fourth except 
thorium. Most of the other elements when exerting their group 
valencies form practically non-conducting halides. The B ele- 
ments follow the same general lines, but the conductivities are 
smaller. The only chlorides with conductivities between 1 and 
10~ arc beryllium chloride (0-0082), zinc chloride (0-01) and 
mercuric chloride (0-0008). The nature of the linkage is largely 
dependent on the conditions, and many of the chlorides which 
are bad conductors in the fused state are highly ionized in water, 
such as hydrochloric acid, aluminium chloride, and stannic 
chloride. The general conclusions are those required by Fajans' 
theory, lomzation being promoted by small charge and large size 
of the cation. 

The influence of the size of the halogen is in the opposite 
direction ; the larger it is, the more readily it should form 
covalencies. The atomic volume, being derived from the covalent 
free halogen, throws little light on the size of the ion. But the 
X-ray measurements of the fully ionized crystals of the alkaline 
halides show clearly that the diameter of the chlorine ion is 
about 1 A.U. greater than that of the fluorine ion, and that a 

3 ofu p 


further increase of about 0-4 A.U. occurs when we go from 
chlorine to bromine and from bromine to iodine. We should thus 
expect that fluorine would ionize most readily, and that iodine 
would have the strongest tendency to form covalent compounds. 
This is in complete agreement with observation. There are many 
metals, such as aluminium, tin, and mercury, of which the 
fluorides have the high boiling-points of salts, while the other 
halides behave as covalent compounds, and a further example is 
found in the halides of silver, of which the chloride and bromide 
have in the crystal an ionic lattice, while the iodide (in one form 
at least) has a molecular lattice. The same thing is seen in the 
formation of higher covalencies : those of five and six are limited 
to iodine, and a covalency of three, apart from the oxy-acids, is 
rare with bromine, almost unknown with chlorine, and quite 
unknown with fluorine. 

As is usual, the affinity for hydrogen falls off greatly as the 
atomic number increases, as is shown by the familiar change in 
the heat of formation of the gaseous hydrides (HF + 38-5, 
HC1 + 22-0, HBr + 8-6, HI - 6-4 kgr. cals.). The great affinity 
of fluorine for hydrogen explains some of its more puzzling 
peculiarities. The affinity for oxygen increases on the whole, but 
irregularly : fluorine forms no compounds in which it is attached 
to oxygen (no oxides and no oxy-acids) ; chlorine forms oxides 
(unstable, and including the anomalous dioxide C1O 2 with its 
odd molecule), and oxy-acidsup to the very stable perchloric acid; 
bromine forms no oxide and no perbromic acid, and even in the 
HXO 3 stage seems to have less affinity for oxygen than either 
chlorine or iodine (heats of formation of HXO 3 aq. : HC1O 3 
23-0, HBr0 3 12-5, HI0 3 56-0 kgr. cals.). Iodine forms a stable 
pentoxide, and very stable oxy-acids up to H 5 IO fl , in which the 
iodine is attached to six oxygen atoms. The refusal of bromine 
to form to 4-covalent HXO 4 , while chlorine and iodine do so, 
may be compared with the instability of other members of the 
same period, such as vanadium, chromium, and arsenic, in the 
,'HrCovalent state. 

In their covalent compounds the halogens show in general a 
progressive change of properties. As with the alkali metals, the 
highest observed covalencies are definitely below the theoretical 
maxima ; this is shown by the following list, m which the 
maxima according to the covalency rule are added in brackets : 
fluorine 2 (4), chlorine 4 (6), bromine 8 (6), iodine 6 (8). In their 
general behaviour, chlorine and bromine are similar, and differ 

Fluorine 291 

in many ways from fluorine on the one hand and iodine on the 
other. Fluorine has four marked characteristics : (1) its great 
tendency to ionization, already mentioned ; (2) its great affinity 
for hydrogen ; (3) its very low covalencies ; (4) its tendency to 
combine with other atoms up to their highest covalency values. 
These sometimes conflict with one another. The only compound 
in which it certainly has a covalency greater thajn one is the 
polymerized hydrofluoric acid. This acid at its boiling-point 
(19-4) has a vapour density approaching that of H 4 F 4 , although 
at 90 it is practically entirely HF, and there is no evidence of 
the existence in water of any molecule containing more than 
two fluorine atoms. The highest polymer must contain the 
grouping F-H-s-F H-s-, with 2-covalent fluorine, but this is 
evidently unstable. In water hydrofluoric acid occurs as the 
single and double molecules HF and HgFa, or their ions. It has 
been shown that while the polymerized form is a strong acid 
H[F 2 H] and is wholly ionized, the true dissociation constant of 
the simple HF is only 7 x 1CT 4 (about three times that of formic 
acid, and about half that of monochloracetic), so that the 
weakness of hydrofluoric acid as compared with the other halogen 
acids is only partly explained by its polymerization. This 
conclusion, that whereas the other halogen hydrides are practi- 
cally completely ionized in water, hydrogen fluoride is mainly 
covalent, is particularly surprising in view of the greater 
tendency in general of fluorine to ionization, which is established 
both practically and theoretically. It would seem that this is 
overcome in the case of the hydrogen compound by the unusual 
strength of its covalent link to hydrogen. The same thing seems 
to account for the peculiar tendency of the fluorine ion to 
hydrate, as is shown by the existence of hydrated fluorides of 
potassium and silver, two metals of which the salts are normally 
anhydrous : the fluorine ion, being negative, will of course 
attach itself to the hydrogen of the water. The last peculiarity of 
fluorine is that while its own covalency is unusually low, it tends 
to bring out the highest covalencies of the other atoms with 
which it combines. This is illustrated by such compounds as 
[F 2 H] ", AsF 6 , IF 5 , SF 6 , SeF 6 , and OsF 8 , to which the other 
halogens offer no analogues. The cause of this may very well be 
the small size of the fluorine atom ; but whatever the cause, the 
fact is very marked. 

The other halogens readily assume a covalency of more than 
one, and do so on the whole with greater ease as the atomic 


number increases. Many such compounds are derived from the 
simple octet by co-ordination, as in 

<d H-Q. -O 

H-0-C1->0, H-O-CIC and >C1< , 


of which the last is the most stable. These types are also formed 
by iodine, ai\d all except the last by bromine. The normal form 
of periodic acid (and the periodatesi) is different, but the 4-covalent 
structure must be assumed, for example, in the crystalline HI0 4 , 
and hi anhydrous K[IOJ. Iodine can also assume a covalency 
of two in a different way (still retaining the octet), by losing 
an electron and forming an iodonium ion, as in the aromatic 
derivatives [Ar 2 I]X: the corresponding hydroxide is a strong 
base. These compounds are structurally analogous to the ammo- 
nium and sulphomum bases ; they are not very stable, and are 
almost if not quite limited to the aromatic compounds. No 
other halogen can behave in this way. Periodic acid shows 
a tendency, precisely like telluric acid, for the iodine to pass into 
the 6-covalent form, with the expansion of the octet to a duodecet : 
it crystallizes from wa'ter as H 5 I0 6 (although this can be dehy- 
drated to HI0 4 ) and gives a series of salts M' 6 I0 6 = (MO) 5 1--0, 

and another series M' 3 I0 5 = (MO) 3 I^_. (these are written for 

convenience in the non-ionized form), as well as more complicated 
condensed types, such as M' 4 I 2 9 . In these compounds the 
iodine has the normal core, its E.A.N. being (2) (8) (18) (18) 6, 6 : 
that of tellurium in the tellurates (p. 286) is the same. 

So far, the structures of the halogen atoms in their compounds 
are of the normal type. There are, however, other compounds 
in which the structure can only be explained on the assumption 
that two of the original seven valency electrons are inert, and 
behave as part of the core, which takes the form (2) (8) (18) (18) 
(2). This behaviour is to be expected, from the analogy of other 
groups, among the heavier members of the series, and in fact 
such compounds are almost confined to iodine. The absorption 
of two of the valency electrons into the core would make the 
element behave like one of the fifth group such as antimony, 
just as it makes tellurium behave somewhat like tin. The most 
familiar examples of such compounds are the polyhalides, such 
as K[I 3 ] and Cs [IC1J. The ion of the latter evidently has the 

structure I<(pp and this is confirmed by X-ray observations ; two 


of the halogen atoms are in the normal 1-covalent form, and the 
third, which is in an abnormal state, links them together. This 
third atom having gained three electrons, one from the charge 
and one from each of the other two halogen atoms, has ten 
electrons outside the normal core of 46, four of them being 
shared. The resulting form (6, 2, 2) a mixed decet is, as we 
have seen, almost unknown except when two of the unshared 
electrons can be regarded as patet of the core. Since the inertness 
of the first pair increases with the atomic weight, the heaviest 
halogen in a mixed perhalide will always form the link. Any 
halogen except fluorine can form part of a perhalide ; the 
stability is greatest if one of the atoms is iodine, much less if the 
heaviest is bromine, and very small in the trichlorides. More 
complicated perhalides (up to [ha! 9 ]~) are known, but few of them 
have been shown to exist in any but the solid state. A similar 
structure must be assumed for such compounds of trivalent 

iodine as the trichloride IC1 3 , the aryl iodide-chlorides Ar I<( r , , 

the lodoso-compounds Ar 1=0, and their acetates 

/0-CO-CH 3 


On the assumption of a core of 46 + 2," all these have mixed 
octets (2, 3, 3). The analogy to the fifth group elements is further 
shown in the 5-covalent pentafluonde IF B (boiling-point 97, 
vapour stable up to 400), in which the iodine has the E.A.N. 
(46+ 2) 5, 5. The iodoxy-compounds ArIO 2 can either be 

written as 4-covalent Ar 1^ , on the analogy of the nitro- 
compounds, or as 5-covalent Ar 1^ . In either case they 

have the increased core of 48. 

An unexplained anomaly is the formation of double salts from 
iodine trichloride. If the iodine in this has the structure (48) 
(2j 3, 3), it should be capable of acting as a donor but not as an 
acceptor. It forms, however, a series of salts of the type KflClJ, 
and the stability of the trichloride in strong hydrochloric acid 
suggests the formation of an acid H[IC1 4 ]. In this ion the central 
atom has 12 electrons in addition to a core of 46, of which 8 are 
shared. Even if we assume that two of them are inert we are 
left with the mixed decet (2, 4, 4), to which there is scarcely any 

Subgroup VII A : Manganese, Masurium, Rhenium. 

The last two elements have recently been discovered by means 
of their characteristic X-rays in platinum ores, m columbite, and 
probably also in manganese ores ; but scarcely anything is 
known of them except that they are less easily precipitated by 
hydrogen sulphide than manganese, and that they form volatile 
oxides. Our knowledge of the subgroup thus rests on the be- 
haviour of manganese. 

Manganese exhibits valencies of 2, 3, 4, 6, and 7 : that is, the 
third quantum group in the core can contain 13, 12, 11, 9, and 
8 electrons : the core (2) (8) (10), which docs not occur with 
manganese, is very unstable with chromium (Cr iv ). In the two 
highest valencies it is definitely acidic, in the two lowest (and to 
a considerable extent in its quadrivalent compounds) it is 
metallic. It resembles the halogens m its highest state of oxida- 
tion only, the permanganates being isomorphous with the 
perchlorates, and having nearly the same molecular volumes. 
Their chemical properties are, of course, very different, as the 
permanganates are readily reduced owing to the ease with which 
the valency electrons are absorbed into the core, which cannot 
happen with chlorine. A valency of six occurs in the manganates, 

as Na 2 |^ 5 Mn ^0 J > tne hydrates of which are isomorphous with 

those of sodium chromate, and one of them with the correspond- 
ing sulphate. This valency is less stable, as the ion readily passes 
into that of the permanganate and manganese dioxide. The 
compounds of quadrivalent manganese are only known either in 
insoluble forms such as manganese dioxide, or in complexes such 
as K 2 [MnCl fl ], which readily pass into forms of lower valency 
with loss of chlorine : no quadrivalent ion is known. The definite 
formation of cations is first observed m the next lower valency, 
that of trivalent manganese. This is also unstable, and the salts 
tend to hydrolyze to insoluble oxides or hydrates unless they are 
protected by complex formation. The salts of divalent manganese 
are stable, and are much less hydrolyzed ; in acid or neutral 
solution they are not affected by air, but in presence of alkali 
air rapidly converts them into more highly oxidized products. 
The behaviour of manganous and manganic salts is very similar 
to that of ferrous and ferric. The general tendency in the series 
of elements from titanium to nickel is for the stability of the 
divalent form as compared with the trivalent to increase with 

Group VIII 295 

rise of atomic number, but in respect to this property manganese 
does not quite come in its place. The divalent form is on the 
whole rather more stable in manganese than in iron. 


Elements and atomic volumes : 

VIII 1. 

VIII 2. 

vm 3. 


Co 27 

















The three transitional triads, conventionally regarded as a 
single group, should properly be divided vertically into three 
series, distinguished, according to the number of electrons they 
have in excess of those in the preceding inert gas, as groups VIII, 
IX, and X. As, however, the convention is so firmly established 
these three divisions may be called subgroups VIII 1, VIII 2, 
and VIII 3. 

The common view that the elements of a triad resemble one 
another far more closely than they do their immediate prede- 
cessors and successors is the result partly of this traditional 
grouping (which was itself largely due to a desire to secure 
greater apparent symmetry in the periodic table) and partly of 
the fact' that there are no typical or B elements with which to 
compare them. Actually there are considerable differences 
between the successive members of each triad : the three vertical 
series have sufficient individuality to have enabled chemists to 
assign the correct chemical order to cobalt and nickel before 
their atomic numbers were known ; and at the same time these 
elements have many analogies both with the preceding elements 
and also with copper and gold in their higher valencies. 

As will be seen from the table on p. 48 there is a difference 
between the three horizontal rows in the structure of the normal 
atom : 

Fe (C) (14) 2 Co (C) (15) 2 Ni (C) (16) 2 

Ru (C) (15) 1 Rh (C) (16) 1 Pd (C) (18) - 

Os (C) (14) 2 Ir (C) (15) 2 Pt (C) (16) 2 

296 Group VIII 

In the first and third rows the outermost quantum group always 
contains two electrons, while in ruthenium and rhodium one, 
and in palladium both, of the last two electrons are in the previous 
electronic group. This difference in the stability of the penulti- 
mate group has a marked effect on the elements next after the 
triads, in the refusal of silver to follow copper and gold in reach- 
ing a valency greater than one ; but it is less easy to trace its 
chemical influence on the elements of the triads themselves, 
probably because their valency relations are altogether more 
complicated. It is obvious that in solid elementary palladium 
the structure cannot be the same as in the isolated atom ; the 
metal is a conductor, and must be formed of positive ions (in 
which the 18 group has broken down) and electrons. 

Certain progressive tendencies may be observed both in the 
horizontal and in the vertical series. In every vertical series we 
find, as in the A elements of the preceding groups, that with an 
increase of atomic number the lower valencies become less and 
and the higher more stable. This makes the elements become 
less metallic in their compounds as a whole, since the electro- 
positive behaviour is connected with the lower valencies. Further, 
even when they have the same valency the successive elements 
of any vertical series show an increasing tendency to complex 
formation, as may be seen by comparing the compounds of 
divalent nickel, palladium, and platinum. 

In the relations of the three vertical series to one another the 
most remarkable differences are in the increasing stability of 
the divalent as compared with the trivalent form, and the 
disappearance (except to a very limited extent with the heaviest 
member of each series) of all valencies greater than four, after 
we leave the first series. 

It may be pointed out that none of these elements appears to 
be capable of a valency of five. 

Subgroup VIII 1 : Iron, Ruthenium, Osmium 

This subgroup is distinguished by the frequent occurrence 
of valencies of six and eight, especially in the heavier members. 
As these elements have eight electrons more than an inert gas they 
might be expected to show a valency of eight, especially in 
8-covalent compounds, which could be formed directly without 
co-ordination. By the covalency rule this value is possible for 
ruthenium and osmium, but not for iron. Accordingly, we find 

Cobalt, Rhodium, Iridium 297 

that osmium (alone among elements) forms an octofluoride 
OsF 8 (B.Pt. 47-5). It is at least probable that we should assign 
a similar 8-covalent structure to osmium in the tetroxide Os0 4 , 

V ^ \ y 

and write it ^Os and not /Os\ , or in any mter- 

/ V ^ N 

mediate form. This is supported by the fact that ruthenium, 
which also can be 8-covalent, likewise forms a volatile tetroxide 
(B.Pt. 101 at 188 mm.), while iron, which is limited to a co- 
valency of six, does not. The argument from the parachor 
against the 8-covalency of osmium in the tetroxide is, as we 
have seen (p. 128), inconclusive. 

The chief change as we descend the series is the diminishing 
stability of the lower valencies and of the simple ions. The most 
stable valencies of iron are two and three (ferrous and ferric), 
practically the only other being six in the ferrates KafFeOJ. 
The chief valencies of ruthenium are three and four, and the 
next most stable six and eight, while two and seven (but not five) 
rarely occur. In osmium the most stable are six and four, and 
then eight : three occurs rarely, but no others. 

Subgroup VIII 2 : Cobalt, Rhodium, Iridium. 

This subgroup is remarkable for the stability of the trivalent 
state (especially in complexes), and for the absence of the higher 
valencies, nothing being known above three for cobalt, four for 
rhodium, and six for indium. 

The behaviour of cobalt illustrates the effect which complex 
formation may have on the stability of a particular state of 
valency. The only form of simple (or hydrated) ion which is 
stable is the cobaltous : the only simple cobaltic salt known, the 
sulphate Co 2 (SO 4 ) 3 , rapidly changes in solution into the cobaltous 
salt, with evolution of oxygen; but in the 6-covalent form (as 
in the ammmes) the cobaltic ion is extremely stable. 

Rhodium occurs mainly m the trivalent form, which resembles 
the cobaltic ion in giving an enormous number of 6-covalent 
co-ordination complexes, but differs from it in being stable also 
as the simple ion. It is doubtful whether rhodium is ever 
divalent, but it can occur (which cobalt cannot) with a valency 
of four. 

Iridium again is most stable in the trivalent state, practically 
always forming complexes. Higher valencies of four and six are 

3 6 ' Q q 

298 Group VIII 

known, and compounds of divalent and even univalent indium 
have been described, but their existence is doubtful. 

Subgroup VIII 3 : Nickel, Palladium, Platinum. 

All the members of this subgroup are stable in the divalent 

The comparison of cobalt and nickel illustrates the increase of 
stability of the divalent state of these elements with rise of 
atomic number. It is doubtful whether trivalent nickel exists 
at all. In near^fall its compounds nickel is divalent, but a red 
complex cyanide of univalent nickel K 2 [Ni(CN) 3 ] has been 
prepared. Palladium again is nearly always divalent (and usually 
complex), but compounds are known in which it is tri- and quadri- 

Platinum is comparatively stable in the divalent state, but 
more so in the quadrivalent ; this is the normal increase of 
stability of the higher valencies with increase of atomic number 
in any subgroup. The complex derivatives of di- and quadri- 
valent platinum have been investigated in very great detail, 
and they illustrate the influence of the covalency on the stability 
of the valency. Nearly all the complexes formed by divalent 
platinum are 4-covalent (the four groups, as we have seen, lying 
in a plane), while those of quadrivalent platinum have a co- 
valency of six. 

There are also a few compounds in which platinum has a 
valency of six, and some in which it appears to have a valency 
of three. 



The more important references are printed in thick type 

ABEQG, R., rule of eight, 53 
Abnormal liquids, 133 
Absolute valency, 182 
Acceptor liquids, 187 
Acceptors, 116 

Acetates, simple and complex, 264, 

Acetic acid, polymerization of, 253 
Acetylacetonates, hydrated, 169 
Acetylacetone, 120 
Acidity and chelation, 250 
Aggregates, crystalline, 186 

Alkali metals, 258, 259 
alkyl derivatives of, 154 
magnetic moment of, in vapour, 

Alkaline earth metals, 263 

Aluminium, 266 

stereochemistry of, 224 
structure of atom in compounds, 

Alums, structure of, 188 
Amine oxides 
' co-ordinated, 71 
optical activity of, 220 

as pure donors, 138 
basicity of,-97 
Ammines, stability of, 200 

combination with salts, 201 
( compounds with cuprous and sil- 
ver hahdes, 208 
of crystallization, 200 

Ammoniates, lattice energy of, 202 

bases, molecular state of, 97 

true dissociation constant of, 97 

ion, hydration of, 194 

radical, 65-8 

AMPERE, theory of magnetism, 


ANDRADE, E. N. da C., 31, 204 

Anions and cations, mutual influence 

in hydration, 196 
Anions, hydration of, 194 
Antimony, 278 

pentachloride, parachor of, 180, 


Arc spectra, 36 
ARRHENIUS, S.,sl, 55, 94 
Arsenic, 278 

4-covalent, stereochemistry of, 225 

6-covalent, stereochemistry of, 


Association, molecular, Chapter 
VIII, 132 

and conductivity, 183 

and co-ordination, 134 

and dielectric constant, 185 

and donor atoms, 149 

and lonization, 187 

and the mixture law, 186 

and solubility, 188, 144 

and volatility, 185 

cryoscopic evidence of, 149 

of water, 185 

two kinds of, 134 
ASTON, F. W., 102 
Atomic and molecular magnetism, 

Chapter XII, 204 
Atomic number and nuclear atom, 

Chapter 1, 1 
Atomic number, 7 

effective, 163 

of inert gases (Rydberg), 28 
Atomic rays, magnetic moment of, 


composition of, 8 

core of, 63, 170, 176 

dimensions of, 9 

table of structures, 48-50 

types of, 45 
Auric compounds, 262 
AUWERS, K., 184, 148 
Azimuthal and radial quantum num- 
bers, 25, note 
Azo-dyes and chelation, 235 



/3-Diketones, 120, 147 

/3-Rays and atomic structure, 4 

BACK, E., 84 

BAEYEH, A., Strain theory, 99, 236 

BAIN, A. M., 221 

BALMER, J. J., 21, 36 

BARKLA, C. G., 6 

BAUDISCH, O., 215, 217 

BAUER, E., 211 


BENNETT, G. M., 251, note 

Benzyl, sodium, 200 

BERTHOUD, A., 130 

Beryllium, 263 

basic acetate, 222 

ion, hydration of, 192 

stereochemistry of, 221 

structure of, 38 

conductivity of fused halides, 105, 

solvation, 187, 197, 201, 202 

references, 98, 169, 280 
Biscnorr, C. A., 220 
Bismuth, 278 

inert pair of electrons in, 181, 278 
BOESEKEN, J., 222 

atomic structure, theory of, 
Chapter II, 14 

atomic structure and covalency 
rule, 167 

helium, metastable form of, 257 

hydrogen atom, theory of, 14 

magneton, 207 

'normal atom', 47 

periodic table, 39 

references, 34, 40 

theory of atom and periodic classi- 
fication, Chapter III, 25 
Boric acid, weakness of, 266 
BORN, M., 202 
Borofluondes, 68, 69 
Boron, 265 

co-ordination of, 67 

hahdes, abnormal volatility of, 

hydrides, structure of, 103 

maximum covalency, 155 

stereochemistry of, 222 

structure of, 88 

BOSE, E., 184 

Bo WEN, I. S., 37 

Brackett series of hydrogen, 21 

BRAGG, W. H. and W. L, 88, 90, 92, 


BRAZIER, S. A., 252 
BREWER, F. M., 145, 155 
BROEK, A. van den, 7 
BROWN, F. S., 135 
BRUHL, J. W., 252 
BURGESS, H., 221 
BURROWS, G. J., 225 
BURY, C. R. 

association, 135 

atomic structure and the periodic 
table, 29 

CABRERA, B. } 213 
Cadmium, 263 
CALLOW, R. K., 147, 152 
Carbon, 270 

divalent, 180 

stereochemistry of, 219 
Carbonate-compounds, 243 
Carbonyl compounds, diamagnetism 

of, 216 

Carbonyl group, hydration of, 195 
Carboxyl group and co-ordination, 


Cations, hydration of, 192 

and amons, mutual influence in 

hydration, 196 
Cerium, 267 

hydrate of acetylacetonate, 169, 


CHAD WICK, H., 162 
Chelate compounds 

and acidity, 250 

nature of, 119 

of azo-dyes, 235 

of mordant dyes, 234 

of sodium, 146 

of thallium, 146 
Chelate rings, Chapter XIV, 233 

evidence for, "2'M 

in /i-diketones, 147 

in ortho-substitutcd phenols, 147 

types of, 239 
Chlorine, 292 



Chromium, 287 

comparison with sulphur, 80 
CLARKE, S. G., 228 
CLINCH, J. A., 169 
Cobalt, 297 

4-covalent, supposed plane sym- 
metry of, 280 

of rare earth metals, 41 

of transitional elements, 48 

Combination principle, Ritz's, 20 

Complete groups, definition of, 171, 

Complex ions, magnetism of, 214 


of associated liquids, 133 
of fused halides, 105, 289 

Co-ordinate links, 52 

conditions of formation, 116 

definition of, 60 

dipole character of, 71, 122 

Lewis's mechanism of, 59 

properties of, 121 

symbol of, 60 

weakness of, 121 

Co-ordination, Chapter VII, 109 
and association, 134 
and the carboxyl group, 252 
and change of electrovalency, 111 
and dielectric constant, 124 
and molecular volume, 124 
and parachor, 127 
and volatility, 123 
electronic interpretation of, 112 
number, Werner's, 109 
of hydrofluoric acid, 72 
of hydrogen, 72, 117 
of ions, 69 
of water, 72 
Werner's theory of, 109 

Copper, 260 

magnetic moment of, in vapour, 


stereochemistry of, 220 
transitional properties of, 42 

Core, atomic, 63, 170, 176 

distribution of electrons in, 165 
fixed, changes of valency with, 


of transitional elements, 77, 176 
stable forms of, 76 

COSTKR, D, 47 


actual and possible, 161 
and electrovalency, Chapter VI, 


and the periodic table, 104 
criteria of, 84, 86 
isomerism a proof of, 86 
odd, 161 

stereoisomerism a proof of, 86 
transition to electrovalency, 92 
volatility a proof of, 87 
Covalency maxima, Chapter IX, 152 
and the Bohr theory, 167 
in first short period, 153 
of boron, 155 
of fluorine, 153 
of hydrogen, 153 
of nitrogen, 154 
Covalency rule, 152 
and hydrolysis of halides, 156 
apparent exceptions, 160 
Covalent links 
Fajans's theory of formation, 104, 

101, 202 

of one electron, 102 
of two electrons, 57 
Cryoscopic evidence of association, 


Crystal structure 
and iomzation, 90, 92, 106 
and ionized lattices, 91 
and X-rays, 90 
ammonia of, 200 
water of, 189 
Cupnc compounds, 261 
Cuprous salts, conditions of stability 

of, 260 
CURIE, P., 205, 211, 212, 218 

DALTON, J., 1 
DARWIN, C. G., 9 

Theory of strong electrolytes, 94, 

X-rays and crystal structure, 90 

DELEPINE, M., 223 
DHAR, N., 190 
Diamagnetism, 204, 206 

of carbonyl compounds, 216 

of simple ions, 212 



Diamine compounds, 243, 247 
Diazo-compounds, stereochemistry 

of, 221 
Dielectric constant 

and association, 135 

and ionization, 132 

effect of co-ordination on, 124 
Dimensions of atom, electron, and 

proton, 9 
Dipole character of co-ordinate link, 

71, 122 
Displacement law 

electronic, 66 

radioactive, 7 

spectroscopic, 37 
Dissociating solvents, 136 
Dissociation constants of ammonium 

bases, 97 

Divalent carbon, 180, 272 

definition, 116 

donor atoms and association, 149 

donor liquids, 137 

pure donors, 187 
Double salts, 118 
Double water molecules, 188, 199 
Doubly linked atoms, rotation of, 


DREW, H. D. K., 119 
DRUCKER, K., 135 
DRUDE, P., 52, 55 
DUFF, J. C. } 251 
DUMAS, J. B. A., 51 

Effective atomic number 

and paramagnetism, 215 

definition, 163 

of platinamnnncs, 165 

of transitional triads, 166 
Effective valency, 114, 104 
Eight-membered rings, 251 
EINSTEIN, A., 19, 209 

strong, Debyc's theory of, 94 

weak, condition of, 93 
Electronic formulae of compounds) 

Electronic increment, 164 


application of, to valency, 52 

charge of, 3 

dimensions of, 9 

displacement law, 66 

groups, subgroups, and grouplets 

of, 31 
mass of, 3 

negative character of, 2 
orbits of shared, 98 
sharing of, Lewis's theory, 56 
spinning, 34 

transference of, in salts, 54 
velocity of, 2 


and covalency, Chapter VI, 83 
change of, in co-ordination, 111 
transition to covalency, 92 

Energy levels in atom, 83 

EPHRAIM, F., 197, 200 

Ethers as pure donors, 187 

Ethyl, sodium, 260 

EWBANK, E. K., 147, 148, 197, 249 

Excessive hydration, 198 


radioactive displacement law, 7 

theory of ionization and cova- 
lency formation, 104, 108, 117, 
158, 157, 191, 192, 196, 201, 
258, 259, 289 

laws of electrolysis, 1 

diamagnetism, 204 
Ferromagnetism, 205 
Fine structure of hydrogen lines, 

28, 34 

FINN, O., 221 
Five-membered rings, 245 
Fluorides, hydration of, 196, 290 
Fluorine, 291 

maximum covalency of, 153, 290 

FdSTERUNG, K., 90 

Forced valency, 178 
FORCRAND, R. de, 187 
Four-membered rings, 243 
FOWLER, A., 22, 23, 37 
FOWLER, R. H., 46, 98, 101 
FRENCH, H. S., 254 
FRENKEL, J., 34 
FRICKE, R., 190 



Gallium, 267 

inert, 257 

paramagnetic, 211 
GEIGEH, H., 5 

GERLACH, W., 204, 208, 209 
Giant molecules, 90 
Glycocoll, 245 
Glyoxal, 245 


Gold, 260, 262 

magnetic moment of, in vapour, 


GOTTS, R. A., 222, 226 

Gngnard reagent, 117 

GRIMM, H. G., 42, 46, 92, 105, 107, 
179, 182, 202 

Grouplets, electronic, 81 

Groups, electronic, complete, de- 
finition of, 171 

Hafnium, 274 

hydrate of acetylacetonate of, 169 
theoretical importance of, 44 

HALBAN, H. v., 96 

Hal ides 

fused, conductivity of, 105, 289 
hydrolysis of, and covalency rule, 

per-, 292 

polymerized, structure of, 244 
volatility and structure of, 88 

Halogens, 289 

HANTZBCH, A., 96, 221, 230 

HARRISON, P. W. B., 228 

HARTREE, D. R., 46 


effusion and solubility, 140 
of solution, apparent, 148 


Helium, 257 

metastable state of, 257 
spectrum series of ionized, 22 
structure of, 27 

HELMHOLTZ, H. v., 1 

HEVESY, G. v., 169 

Hexafluondes, action of water on, 

HlLDEBUAND, J. H., 189 

HOFF, J. H. van 't, 55, 110, 182, 219, 


HOLBOYD, G. W. F., 162 
HOLTZ, J., 154 
Hot spark spectra, 37 
HUCKEL, E., 190 
HUND, F., 46, 214 

of acetylacetonateg, 169 

of inert gases, 187 

of paraffins, 187 

solid, 191 

and size of ions, 197 

excessive, 198 

in solution, evidence of, 190 

mutual influence of ions in, 196 

of anions, 194 

of cations, 192 

of ions, mechanism, of, 189 

of ions of transitional elements, 

of salts, 189 

of salts, and vapour pressure of 

solutions, 197 

of boron, structure of, 108 

volatility and structure of, 87 
Hydrofluoric acid, 291 

co-ordination of, 72 
Hydrogen, 258 

co-ordination of, 72, 117 

covalency maximum of, 153 

ion, hydration of, 193 

negative ion of, 64 

position in periodic table, 63 

replaceability by radicals, 101 
Hydrogen atom 

Bohr's theory of, Chapter II, 14 

fine structure of lines of, 23, 24 

magnetic moment of, 210 

spectral series of, 21 

stationary states of, 20 

of hahdes, and the covalency rule, 

of silicon chains, 159 
Hydroxyl ion, hydration of, 195 
Hypophosphoric acid, 279 

Ideal liquids, 132 
Increment, electronic, 164 



Indium, 267 
Inert gases, 257 

atomic numbers of, 28 

hydrates of, 187 

importance of, 28, 54 
Inert pair of valency electrons, 178, 

179-81, 265, 267, 270, 273, 278, 

285, 292. 

INGOLD, C. K., 286, 287 
Iodine, 202, 293 
lodomum compounds, 67 

and association, 187 

and crystal structure, 90-2, 106 

and dielectric constant, 182 

and the periodic groups, 106 

factors determining, 76 

Fajans's theory of, 104 

gaseous, 10 

of platmamnunes, 111 
Ionized links, 52 

Ionized molecules, criteria of, 84-0 

complex, magnetism of, 214 

co-ordination of, 69 

distribution in periodic table, 104 

mechanism of hydration of, 189 

mutual influence of, on hydration, 

simple, magnetism of, 211 

size of, and hydration, 197 

tests for, 85 

XO 4 , structure of, 59, 60 
Indium, 297 
Iron, 296 

carbonyl, diamagnetic, 216 

magnetism of, 205 
Isomerism a proof of covalency, 86 
Isotopes, nature of, 11 

of lead, properties, 11 

JACKSON, L. C., 215 
JEANS, J. H., 14, 15 
JOB, A., 169 

J6KGENSEN, S. M., 230 

JONES, H. O., 220 
Joos, G., 104 

KELVIN, Lord, 1 
KENYON, J., 22*8 
KIPPING, F. S., 159, 225 


KLEMM, W., 93, 105 
KOPP, H., 124, 125 

spectroscopic displacement law, 

theory of polar links, 53-5, 57, 58 


Theory of magnetism, 205, 206 
LANGMUIR, I., 18, 57, 62 
LAPORTE, O., 46 
LATIMEB, W. M., 98 

energy of ammoniates, 202 

ionized crystal-, 91 
LAUE, M. v., 90 
Lead, 273 

inert pair of electrons in, 181 

isotopes of, 11 
LE BEL, J. A., 219 
LE BLANC, M., 130 
LEMBERT, M. E., hydration of salts, 

191, 194, 196, 199 

negative hydrogen ion, 64 

octet theory, 62 

theory of non-polar link, 56-9, 
71, 88, 95 

references, 133, 159, 258 
LEWIS, N. B., 193 

LlNDEMANN, F. A., 17, 34, 190 

Links, co-ordinate 

conditions of formation, 116 

definition of, 60 

dipole character of, 71, 122 

Lewis's theory of, 59 

symbol for, 60 

weakness of, 121 
Links, covalent, Lewis's theory of, 

Links, electrovalent, Kossel's theory 

of, 54 

Links, semi-polar, 60, 71 
Links, three types of, 52, 61 

associated, conductivity of, 133 

ideal, 132 

miscibility of, 138 

normal and abnormal, 133 

'polar' and 'non-polar 1 , 133 



Lithium, 2P3 

structure of, 28, 88 

Lithium ion, hydration of, 192 

LOGSTRUP, M., 109 

'Lone pairs', 61 

LORENTZ, H. A., 4 


semi-polar link, 60, 71, 127 
references, 221, 254 

LYMAN, T., spectral series of hydro- 
gen, 21 

McLAY, A. B., 46 

MCLENNAN, J. C., 46 

Magnesium, 263 

structure of atom in compounds, 

Magnetic field, intensity of, near 

nucleus, 204 
Magnetic moment 

of atomic rays, 208 

of electronic orbits, 205, 207 

of metallic vapours, 208 

Ampere's theory of, 204 

atomic and molecular, Chapter 
XII, 204 

and molecular structure, 218 

and structure of carbonyl com- 
pounds, 216 

and structure of nitroxyl com- 
pounds, 216 

Curie's laws of, 205 

Langevin's theory of, 205 

of complex ions, 214 

of simple ions, 211 

Weiss's law of, 212 

Bohr's, 207-8 

Weiss's, 207 

ratio of Bohr's to Weiss's, 208 

distribution of electrons, 34, 35, 

101, 178 

MAMLOCK, L., 230 
Manganese, 294 
MANN, F. G., 228, 248 
Maxima of covalency, Chapter IX, 

Maximum covalency 

and the Bohr theory, 107 


of boron, 155 

of elements of the first short 
period, 158 

of fluorine, 153 

of hydrogen, 153 

of nitrogen, 154 
MAXWELL, J. C., 14, 15 
Means, weighted, 132 
MEISENHEIMER, J., 219, 220, 221, 

225, 228, 229 

valency and the periodic groups. 

periodic table, 74, 75, 256 
Mercurous ion, 264 
Mercury, 263, 264 

inert electrons in, 179 
MEHTON, T. R., 12 
Metallic vapours, magnetic moments 

of, 208 

Metals, mutual solubility of, 151 
Methyl, sodium, 260 ' 
MEYER, J., 154 
MEYER, S., 213 
MILLIEAN, R. A., 18, 37 
MILLS, W. H., 66, 220, 221, 222, 225, 


Miscibility of liquids, 138 
MITCHELL, J. E. H., 162 
Mixed and pure valency groups, 17O 
Mixed octets, 173, 174, 276 
Mixture law and association, 136 
Molecular association, Chapter VIII, 

Molecular volume and co-ordination, 

Molecular volume and Sugden's 

parachor, 124 

Molecules, distinction from aggre- 
gates, 185 
Molybdenum, 288 
Moons, T. S., 97, 250 
Mordant dyes and chelation, 238 
MORGAN, G. T., 119, 222, 233, 234 
MOSELEY, H. G. J., 7, 8, 27 
Muttiplets in spectra, 87 

'Natural Angle 1 , 237, 289 

for singly and doubly linked 
atoms, 238 



'Natural solubility', 141 

Negative vapour pressure curves, 

140, 148 

NERNST, W., 182 
NESTLE, K. T., 280 
NEVILLE, A , 227 
Nickel, 298 

carbonyl, diamagnetic, 216 
magnetic moment of, in vapour, 


NIESSEN, K F., 99 
Niobium, 281 
Nitrate ion 

hydration of, 195 
polymerization of, 198 
Nitric oxide, paramagnetism of, 211 
Nitrites, volatility of, 123 
Nitro-compounds, volatility of, 123 
Nitro-group, structure of, 65 
Nitrobenzene a pure donor, 137 
Nitrogen, 276 

maximum covalency of, 154 
qumquevalent, stereochemistry 

of, 219, 220 

tri- and quinquevalent, 66 
trivalent, stereochemistry of, 221 
Nitrogen dioxide, 279 
Nitroxyl compounds, magnetism 

and structure, 210 
Non-ioni/ed links, 52 
Non-polar links, 52 
'Non-polar 1 and 'polar' liquids, 133 
Normal and abnormal liquids, 138 
'Normal atom' of Bohr, definition of, 

Nuclear atom 

importance of charge, 6, 8 
Rutherford's, 5 
Nuclear atom and atomic number, 

Chapter 1, 1 

charge of, effect on orbits, 38, 40 
intensity of magnetic field near, 


structure of, 12 

Number, atomic, and nuclear atom, 
Chapter I, 1 


formation of, 173 

fully shared, stability of, 175 

fully shared, state of, 101 

mixed, 173, 276 

theory of Langmuir, 62 

theory of Lewis, 62 
Odd covalenciesy 161 
Odd molecules, 178 

paramagnetism of, 211 
OERSTED, H C , 204 
One-electron covalencies, 102 

and parachor, 181 
ONNES, H K., 211 
Optical spectra, 86 
Orbits, electronic 

dimensions of, for hydrogen, 20 

influence of nuclear charge on 38 
40 ' ' 

magnetic moment of, 205, 207 

of shared electrons, 98, 100 

precession of, 25 

types of, 26, 27 

Ortho-substituted phenols, chelatc 
structure of, 147 

Osmium, 296 

Osmium tetroxide, 296, 207 
and covalency rule, 160 
parachor and structure of, 128 


Oxalate ion, hydration of, 195 
Oxalato-compounds, 239 
Oximes, stereochemistry of, 221 
Oxonium compounds, (SO, 283 
Oxygen, 283 

comparison with sulphur, 284 

paramagnetism of, 211 

stereochemistry of, 222 

Palladium, 298 
structure of, 47 

PANKI-H, F , 87 

Paruchor, 124 

and the co-ordinate link, 127 

and the one-electron link, 181 

and size of valency group, 129 

and molecular volume, 124 

and surface tension, 125 

of antimony pentachloride, 130 

of osmium tetroxidc, 1 28 

of phosphorus pcntachlonde, 130 

of sulphur trioxide, 129 

values of, for elements, 126 


hydrates of, 187 

minute solvent power of, 150 




and effective atomic number, 215 

and imperfect electronic groups, 

and molecular structure, 216 

of complex ions, 214 

of gases, 211 

of nitric oxide, 211 

of odd molecules, 211 

of oxygen, 211 

of rare earth metals, 43, 213 

of simple ions, 211 

of transitional elements, 41, 212 
PASCAL, M. P., 206 
PASCHEN, F., 23, 34, 37 
Paschen series of hydrogen, 21 
PAUIJ, W., 208 

PEACHEY, S. J., 219, 226, 227 
Perhalides, 292 
Periodic classification and the Bohr 

theory, Chapter III, 23 
Periodic groups, Chapter XV, 256 
Periodic table 

and atomic structure, 29, 40 

and covalency, 104 

and valency, Chapter V, 74 

Bohr's form of (diagram), 39 

development of (Bury), 29 

distribution of ions in, 77, 104 

Mendeleeff's form modified (dia- 
gram), 75 

Permanganates, 294 
PERRIN, J., 2 
PFEIFFER, P., 198 

Phenols, ortho-substituted, chelate 

structure of, 147 
PHILLIPS, H., 228, 229 
PHIPPS, T. E., 210 

atom, structure of, m compounds, 

pentachlonde, parachor, 180 

stereochemistry of, 225 
PICCABD, A., 211 
PICKERING, 22, 23 
Pickering series of ionized helium, 22 
PLANCK, M., theory of quanta, 15, 

16, 18, 19 
Plane symmetry of 4-covalent atoms 

cobalt (supposed), 280 

platinum, 229 

tellurium, 281 



effective atomic number, 165 

iomzation, 111 
Platinum, 298 
PLATO, W., 223 


Polar links, 52 

Kossel's theory of, 54 
'Polar 1 and 'Non-Polar' liquids, 133 
Polynuclear co-ordination com- 
pounds, 244 

POPE, W. J., 219, 226, 227, 228, 248 
Positive electrons or protons, 6 
Positive vapour pressure curves, 140, 


of orbits of electrons, 25, 26 

of orbits of shared electrons, 100 
PRICE, T. S., 252 

definition of, 6 

dimensions of, 9 
Pure and mixed valency groups, 170 

Quantum number 

azimuthal and radial, 25 

third, 84 

of shared electrons, 100, 164 
Quantum theory 

Bohr's application to atom, 17 

evidence for, 15 

Planck's theory, 16 
Qumones, stability of, 250 note 

Radial and azimuthal quantum 

numbers, 25 

Radioactive displacement law, 7 
RAMSAY, W., 1, 114 note, 135 note 
RATER, R., 225 
Rare earth metals, 266 

colour of, 43 

paramagnetism of, 43, 213 

structure of, 43 
RAYLEIOH, Lord, 1 

Rays, atomic, magnetic moment of, 


REED, J. B., 125 
REIHLEN, H., 280 
Residual rays or Reststrahlen, 90 
Rhodium, 297 
RICHARDS, T. W., 12 

ar 2 



Riesenmolekule, 90 
Rings, chelate 

4-membered, 243 

5-membered, 245 

6-membered, 247 

6-membered, with two double 
links, 248 

7- and 8-merabered, 251 

stability of, and size of atoms, 239 

types of, 239 

RITZ, W., combination principle, 20 
RODEBUSH, W. H., 98 

RONTGEN, W. C., 1 

RosENBonar, E., 215 


Rotation of doubly linked atoms, 99 

RUBENS, H., Reststrahlen, 90 

RUHLE, C., 130 

RUSSELL, A. S., radioactive dis- 
placement law, 7 

Ruthenium, 296 

tetroxide and co valency rule, 100 

RUTHERFORD, E., nuclear atom, 5, 
0, 14 


atomic numbers of inert gases, 28 
constant, 21 
spectral series, 22 

Salicylic acid, structure of deriva- 
tives of, 24*2 

Scandium, 266 
structure of, 40 

Scattering of rays by atoms, 5 


SCHT.KNK, W., 154, 200 

SciIOIiNMATClill, I?., 130 

Sc'iiuLTH, G., 23 li 
Selenium, 285 

oovalency maximum, 150, 158 

.stereochemistry, 227 
Semi-polar link, 00, 71 
Seven-membered rings, 251 
Shuml electrons 

distinction of, in formulae, 104 

Lewis's theory of, 50 

orbits of, 98 

precession of orbits of, 100 

((minium numbers of, 100, 164 
SiiuswiC'K, N. V., 112, 145, 147, 148, 

152, 155, 150, 1!)3, 197 

Sll'AJHAlIN, M., 33 

Silicofluorides, 68 
Silicon, 272 

atom, structure of, in compounds, 

chains, hydrolysis of, 159 

stereochemistry of, 225 
Silver, 260 

hahdes, compounds with am- 
monia, 203 

magnetic moment of, in vapour, 


Six-membered rings, 247 
Size of atoms, 9 

and stability of rings, 239 
Size of ions 

and hydration, 197 

and lattice energy of ammoniates, 


SMEDLEY, I., 252 
SMILISS, S. s 227 
SMITH, H. G., 46 
SMITH, J. D. MAIN, 34, 101, 178 
SMITH, A., 130 

isotopes, 11 

radioactive displacement law, 7 
Sodium, 259 

alkyl and aryl derivatives, 260 

chelatc compounds, 146 
Solubility, 138 

and association, 138, 144 

and heat of fusion, 140 

and structure, 89, 145 

and vapour pressure, 139 

essential conditions of, 189 

mutual, of metals, 151 

'natural', 141 

apparent heat of, 148 

evidence of solvation in, 190 
Solvation, Chapter XI, 185 
KoMMKit, L. A., 42, 44, 45, 46 


atomic structure, 42, 46 

crystal structure and ionimtion, 
92, 105, 107 

definition of valency, 182 

line structure of hydrogen lines, 
"23, 25, 34 

inert pair of electrons, 179 

references, 37, 101, 208 
Space quantization, 209 
Spark spectra, 36 




arc and spark, 86 

displacement law, 37 

hot spark, 87 

multiplets in, 37 

optical, 36 

series of hydrogen, 21 

series of ionized helium, 22 

X-ray absorption, 32 
Spinning electron, 34 
Stability of atomic structures, 38 
Stable valency groups, Chapter X, 

Stannic chloride, ionized or covalent, 


STARK, J., 44, 53 
Stationary states, 18 

of hydrogen atom, 20 
Stereochemical relations, Chapter 

XIII, 219 
Stereoisomensm a proof of coval- 

ency, 86 

STERN, O., 208, 209 
STERN and GERLACH, magnetic mo- 
ments of atomic rays, 209 
STOCK, A., 103 

scheme of distribution of elec- 
trons, 34, 40, 101, 178 

magnetic relations, 204, 215 

references, 206, 208, 209, 267 ' - 

in rings, 238 

theory of Baeyer, 286 
Strong electrolytes, Debye's theory 

of, 94 
Subgroups of electrons, 31 


parachor, 124-31 
references, 65, 153, 228 
Sulphate ion, hydration of, 195 
Sulphato-compounds, 239, 243 
Sulphomum compounds, 283 
Sulphur, 283 

atom, structure of, in compounds, 


comparison with chromium, 80 
comparison with oxygen, 284 
dioxide, a pure donor, 187 
hexanuonde, valency group of, 62 
stereochemistry of, 227 

tricovalent, stereochemistry of, 

trioxide, parachor and structure, 


Sulphuric acid, structure, 286 
Surface tension and parachor, 125 

Tantalum, 281 
TAYLOR, J. B., 210 
TAYLOR, T. W. J., 249, 251 
Telluric acid, structure, 286 
TeUurium, 286 

4-covalent, plane symmetry of, 


Tetrahalides, volatility of, 175 
Thallium, 267 

chelate compounds of, 146 

inert pair of electrons in, 180 

magnetic moment of, in vapour, 


THIELE, J., 250 
Third quantum number, 34 

atomic model, 4, 14, 18 

dielectric constant and ionizing 
power, 132 

the electron and valency, 52 

theory of the electron, 2 
Tin, 270 

stereochemistry of, 226 

tetrachlonde, structure of, 92 
TOWNSEND, J. S. E., 3 
Transference of electrons in salts, 54 
Transition between electrovalencies 

and covalencies, 92 
Transitional elements 

characteristics of, 41 

chemical peculiarities of, 80, 81 

colour of, 41 

copper, transitional properties of, 

core of, 76, 171, 176 

definition of, 45 

form no mixed octets, 174 

hydration of ions of, 216 

in second long period, 42 

paramagnetism of, 41, 212 

stereochemistry of, 223 

Transitional triads (Group VIII), 

effective atomic numbers of, 166 

peculiarities of, 82 
TRAUBE, I., 124, 125 



Triads, transitional, see Transitional 

Tricovalent atoms, stereochemistry 

of, 228 

TROUTON, F. T., 87 
TSCHUGAEFF, L., 238, 247, 248, 240, 


Tungsten, 288 
TURNER, E. E., 225 
TURNER, W. E. S., 182 
Typical elements, resemblance to A 

and B subgroups, 78 

ULLMANN, G., 135 
UNS6LD, A., 34 
Uranium, 288 


absolute, definition of, 182 

and the periodic table, 51, 

Chapter V, 74 
Berzelius's theory of, 51 
chemical evidence for, 52 
changes of, 177, 178 
effective, 114, 164 
forced, 178 

fundamental principles of, Chap- 
ter IV, 51 

groups, pure and mixed, 170 
limits of, 62 
size of, and the para- 

chor, 129 

stable, Chapter X, 163 
Vanadic acid, 281 
Vanadium, 281 
Vapour pressure 
and hydration of salts, 197 
and solubility, 139 
negative curves, 140, 143 
positive curves, 140, 142 
VERNON, R. H., 231 

VlEWEG, E., 221 
VlLLARD, E., 187 


abnormal, of boron halides, 245 
and association, 135 
and co-ordination, 123 
and covalency, 87 
and structure of halides, 88 
and structure of hydrides, 87 
of nitre-compounds and nitrites, 

of tetrahalides, 175 

WAALS, J. D. van der, 122, 134 
WAUL, W., 224 
WALDEN, P., 134, 144 
WARREN, E. H., 06, 220 
WARTENBERG, H. v., 90 

action of, on halides, 156-8 

association of, 135 

co-ordination of polymerized, 72 

double molecules, 188, 190 
Weak electrolytes, condition of, 93 
Weighted means, 182 
WEINLAND, R. F., 255 

law of magnetism, 212, 214 

magneton, 207, 208 
WELO, L. A., 215, 217 note 

chelate compounds, 120, 233, 23-1, 

co-ordination number, 8t, 1(J5 

co-ordination theory, 52,109, 11 1., 

covalency maximum in lirst short 
period, 15.'$ 

stereochemistry of transition ele- 
ments, 22.'}, 220 

water of crvstalli/ation, 100, 187, 
103, 101) 

references, 58,85, 1 85,2-21 ,2!M, 2 1 1- 

WlIITTAKKR, II., 1*25 
WlECIlKUT, K., 2 
WlLKlNS, II., 125 

WiLsnoN, H. II., 101 
WILSON, C. T. H., !1 

WlNJMILL, T. F., 07 
WlSLICKNU.S, J , '2.'JO 

WOOD, R. W., 'J.'J 


absorption edges, U'2 
and atomic structure 1 , J>, 7 
and crystal structure, 00 
spectra, origin of, ,T2 

YOUNG, S., 1:J5 

Zeeman effect, 1- 
Zinc, 263 

stereochemistry of, 220 
JZirconium, 274 

(eott\,c of acctylacetonutc of, 100